some help

While its a pleasure to meet you, I wish it was in a different forum.
Consider couples therapy. Counseling. But most of all, find a way to communicate.
I believe that is the "emotional connection" she is looking for.
Also ask yourself the hard questions.
Are you supportive of her? Do you listen to her? Do you help around the house? (More than a meal and some coffee)
If she can make a rule about when you can have sex, make a rule no phones at or after dinner.
How old are these kids? What trauma would they suffer hearing their parents have sex?
Why was it okay before, but not now?
Find these things out. We are here as an amateur support group.
Sorry you're here.

"If" you are planning on doing anything here, my suggestion (to you both) would be to do it real quickly, and real decisively.
Jump on it with both feet as hard as you can.
Right now.
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The quicker you (both) act the better your chances of nipping this in the bud.
If you let it go, and it takes root, you're fucked.
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If there is not fully committed quick and decisive action taken by you both, it is only a matter of time before your story will read the exact same as the others in here.
And unfortunately, your story reads like that window of opportunity - where you might have some chance of nipping this in the bud - is rapidly closing. If indeed that window hasn't already slammed shut.
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Addendum (after unmatcheds comment below)
You ARE going to have to be prepared to put the marriage on the line over this.
It can't be a bluff. 

Welcome to hell Ricky. bballgirl is right, you were bait and switched. And now you've entered the second circle of ILIASM Shithole Hell: The Hamster Wheel. You have to work on your emotional connection before you have sex? Another excuse, but with far more nefarious purpose. She has given you a demand upon which her willingness to give physical intimacy depends. And this demand is worded in such a broad and nonspecific way that you can never demonstrate you have met it. You can say you've worked on it and she can say no you haven't or you need to work more. How long do you need to work on it, and what outcome are you shooting for? I hate to sound like a corporate jerkoff, but goals have to be specific and measurable. If you were the Chief Accounting Officer and you presented your five year plan to the Board, and your plan was, "To work on improving our profits," you'd be polishing your resume. She has given you a vague goal and no indication of how she wants to get there.

So you do exactly as she designed: you run yourself ragged doing everything you can think of to make her happy, hoping this will count as working on your relationship. And nothing changes. You are a hamster in a cage, running like hell to nowhere on a giant turning wheel.

Then she makes you feel guilty for expressing your need for physical intimacy. Gotta keep that wheel turning. She sets up ridiculous and arbitrary rules like no sex when the kids are home (please) to ensure that she is the one shaping the relationship and you are the one complying.

Now, people on The Hamster Wheel often run for years or decades trying to decipher incomprehensible rules, codes, and demands in the faint hope that maybe their controller will toss them some crumbs of physical affection. Which of course is the worst thing when they do, because it feels like progress when really it's reset sex. Sex to get you off their back for another six months. Sex to make you think you're getting off the wheel.

You say you're close to divorce. I say good. Because you know what? This is bullshit! Do not accept bullshit in relationships. Every year you waste on the wheel is a year you can't get back. Life is not a renewable resource. You only get so much and that's it. And you'll talk here with people who have spent years or decades on the wheel. And every single one will tell you they were not years well spent.

So what do you do? Communicate. But not the way she has come to expect. Not trying to coax some clue out of her as to how you can meet her demands. No, now you will say this is unacceptable. We will decide right now what we are going to do about it. If I come to perceive that this is not fixable, you will be served with divorce papers. I love you and want nothing more than to be close to you in every way. But I cannot and will not live like this.

You have to mean it. It probably won't change anything. ILIASM shitholes rarely change for the better. But at least you can say you communicated. You didn't "try." What a bullshit word. You will have communicated and stepped off the wheel. She can get on board the train or not, up to her, but its pullin' out the station, leaves at 3:09, I'm goin' to Chicago, leavin' my baby behind.

I tried communicating with her last night what's been bothering me. I told her that I love her, but I can't continue to live like this. She just said yeah, me either. So I asked her if she remembered the last time we were intimate. She said I know it's been a long time. I said it was when we went out of town for your birthday in February. So then I asked her that at anytime in the past 4-5 months has she ever wanted to be intimate with me. And she said yes, but we have had so much going on. Then I ask, why haven't you acted on it? I don't know was the reply I got. I said that's not good enough. She says, we'll it's beens so long that it's awkward. That really crushed me. So now it's awkward!? I'm so hurt, confused and angry. So you mean to tell me that the hugs, and kisses, spooning isn't awkward? Just the sex? Bullshit. I can't keep doing this. And to answer someone else's question do I help around the house and the ages of the kids.
We have 2 sons who are 8 and 17. 2 daughters that are 7 and 12.
And my daily routine is as follows:
I pick the kids up from after school, come home and start dinner, get the kids in the showers and get them to bed. We both work full time. Then I pick my 17yo up from work at 11. I also wash towels and wash cloths , the small ones clothes, do the grocery shopping, run to the store for incidentals , etc. Plus my oldest and I maintain the yard which I enjoy. Plus many other things.

Her daily routine is go to work, come home, walk in the door and pet and hug the dogs, go sit in the room. I love her more than I've loved any woman. But damn it, how much longer can this last? I'm so lonely.

I'm to the point to where I've become withdrawn. No more affection from me until I get some affection.

It sounds like you are approaching counter refuser territory.

I did everything around the house to care for it and the kids.
My H went to work, came home - ate, watched tv, coached my son on the weekends. I felt used.

If it's awkward for her it might be difficult for her to initiate but you both need to continue discussing this, counseling would be a good idea, you both need to work towards the goal of reconnecting sexually because you both want to. If you both don't want to then there is no point to be married especially since it sounds like you are carrying 90% of the household responsibility. No sex for all that you do is total bullshit. I left my husband and got a divorce 6 months ago and I'd like to think he regrets not having sex with me at least once a month so I would have stayed and happily carried all of the responsibility BUT my rational self knows that he is happier to have to do his own grocery shopping, cooking, cleaning, etc. rather than have sex with me so everyone is entitled to their happiness. Just don't waste all the time I did to find yours happiness.

On the surface it seems you are pulling your share of the chores at home in addition to bringing in a paycheck. Your comment about how she interacts with the animals but not the family members is perhaps revealing, especially her just sitting in the room. I assume you mean the living room watching TV. It almost sounds as if she is depressed. What parent doesn't interact with their children and spouse at the end of the day?
Several comments have suggested counseling, I agree. But I think one facet of that counseling should be directed at depression to confirm or remove it as a causal factor.  
You are both still engaged and communicating. There is still a window of opportunity to turn this train around. But time is imperative as the longer the sexless aspect continues the less likely it is to be fixable. And when you reach "deal breaker status" then it is no longer fixable and divorce become the destination. She has to be made to know this, that the threat of divorce is real. Often it takes a major shock to the status quo to jolt the train back on to the track. Good luck...