SM and still hopeful.

In your original post, you say you already crossed the line into infidelity. I'd guess you do whatever you did then. If everyone including your W knows divorce is imminent, why do you need to sneak around and avoid social media?

If she has said you are free to fulfill your needs, you are good to survey social media and websites. I mean I wouldn't flaunt it, but you should be able to do it on your own time without harassment. Also, if the kids have moved out, why would you need to be together for them? You can still be there for them, married or not. 

Thanks deadzone75, she says I am free to fulfill but does not really mean it whole heartedly due to past infidelity trauma. She is stuck in the past and will seek payback for it. Add to it she is still very codependent on me for day to day things . She insists I don’t spend any cash from my salary for socializing and meeting potential dates and given our work/life schedule it’s hardly impossible that I get any window to go out alone and socialize . We also share one SUV .
Kids are not an issue. It’s between me and her to have this agreement . Finances wise we are just able to meet paycheck to paycheck using mine and she will pool in at times when there is a shortage but saves most of her paycheck weekly.

i think using websites/ social media is just for asking straight up for a hook up ....
I bet with as many people dealing with this you could find a companion / friend many places and work up to sex.... perhaps they are in dead end marriages as well so they want to be discreet as well.

every day I hear of people especially around the age of kids leaving or left home that are in unfulfilling marriages.
My boss said someone came up to him at the gym .... he is divorced with a GF so not his thing but it is out there.

I suspect Toughtiger has experienced apps as an avalanche of guys who want No Strings Attached sex.
Tinder is the place women up for that kind of thing should go. Anyone up for "The Girlfriend Experience" like you could go there, but you have a shot on all the others as well.
Most women on apps I've seen want some type of companionship activity, though they'll tolerate casual sex from guys ranking 8 and up.

You being flat broke do not qualify for a hookup, so it's good you offer more.

Even so, flat broke is a helluva hurdle and you'll want to offer romance and you'll have a better shot by reaching down the ladder. Choose women your wife's level, then down 2 rungs, and start form there, lowering until you start getting Yes'es. If you can't cope with dating women that aren't conventionally attractive, you stand the risk of wasting tons of time.

Finding someone local lowers your odds all the more. It's a bit early to be adding obstacles and deal-breaking criteria.
When I started outsourcing, I used OKcupid and placed my location 51 miles NE from the suburbs of my home near the second city over and set my range for 50 miles.
This basically gave me a 50 miles radius of women who could see my profile to the NE of my actual location but none of my family friends would see me come up unless they set their range for 75 or 100 miles. (who is willing to do that outside Podunk?)

This landed me a coffee date 20 minutes away. I could ignore the women who were actually close to the location I said I was at.
This may allow you to use apps undetected.

That said. I need to suggest that you own your sordid past, and do your best from here.

Sounds like she's punishing your infidelity with sexlessness that you had the affair to escape.
And you're letting her.
Not bright, for either of you.

She's said for you to go ahead and find a chippy to shtup, but you get zero budget. Not even gas money.
You cover all her expenses except when something unexpected comes up or a particular budget item comes in high for some reason.
You are basically, economically, living as though you were divorced but the judge has demanded you surrender every disposable cent to your ex-wife.

I'd accelerate the divorce as quickly as possible to obtain a spending budget for adult companionship. The wholesome kind.
You seem to be paying penitence for an affair, why exactly?
You eff'd up? Own it. Maye you already did, but she wants to act the bitter ex-wife part before she's even separated.
Not understanding it. Start divorce now. Make amends as possible, if it helps you feel like less of a bastard. I get it. Apologize some more, but you do not owe her permanent celibacy. Men in prison get conjugal visits form their wives. Expecting you to do without outside the walls of jail is delusional.

Alternately, if reconciliation is on the kids' Christmas lists, tell the Mrs. you'd like to provide but that's going to start with a deadline for resumption of intimacy. Even if it's a pinprick, you need light at the end of the tunnel. You can suffer, but not forever.

If she says she's trying to forgive you and not showing much evidence, could she use some help from women who've been there? 
Maybe she might get something from this? hopeforwives.com/
I listen, even though all I had was a coffee date to discuss having an affair with an affable lady I met on OKcupid. (my wife decided to end our sexlessness rather than have me open the marriage)

Perhaps you'll offer to open the marriage and reconcile while you're engaging in ordinary adult behavior.
Explain you'll be using $20 week to pursue an assistant wife (two dates, or one where you treat) and it's not negotiable. If she wants to save $80 a month, the two of you can date at a local free event that will cost nothing. In as much as she expects women to take you up on your penniless adventures, it's not an unreasonable ask.
Bear in mind, the conventional expectation is sex on the third date. If the wife gets to five and still offers nothing, and if you were strangers you'd stop dating her, and she should expect for you to declare the experiment a failure. This can serve as the remainder of your exile in celibacy. Otherwise, it's just a delaying tactic to postpone your resuming an ordinary adult life. No. Just. No.

I'd ask whether infidelity would worsen your position in divorce settlement, but that horse left the barn.
You state legal reasons for not starting divorce, and I'll pry enough to ask for those reasons. 

I'll also refer you to a post about Divorce Financial consultants and Binding Financial Agreements that are the core of future divorce agreements. Get the ball rolling and supply that light at the end of the tunnel for yourself. Mrs. Atlindsexlessguy can widen/brighten it if she wishes. The process takes a while anyway, starting only when you're at the end of your rope will only torture you further.

Mirror child you are spot on.. yes she is she wants to act the bitter ex-wife part before she's even separated. I effed up and owned it till date but there is no remorse for infidelity in my culture unfortunately .

The main reason we are still living amicably as roommates is because we are stuck in the long immigration process for almost a decade and don’t want to risk it for our son or her as it’s tied to my employer .

Thank you for sharing dating tips. Right now I’m down to accepting any form of physical affection even a hug .. rung wise I am thinking above escort level and maybe some one who is in same boat as me just craving physical touch on ongoing basis ..single or divorced or married.
Yes the finances are a mess , so I am leaning towards separation agreement using mediator.

Sorry if I missed the immigration angle.

"We are stuck on immigration for almost a decade"

Divorce would pooch that.

I'm guessing she's a citizen, you aren't? But you are the father of American citizens? 

Checking legal web sites...this is a green card situation? Permanent residency after a decade? Something like that?

Are you sure a wife soaking you for every penny and keeping a running tab of how much you owe her for her own upkeep is not going to file for divorce in year #9?

Have you received legal guidance in terms of rights as a father of American citizens? Maybe there aren't any. I admit I lack background.

You are empty nesters, that suggests the kids are 18 or very nearly so. Custody is not an issue?

heck man, I love America, but is a decade of misery worth staying? Maybe it is. Some countries are in tough shape. Can you get citizenship elsewhere more easily? A reasonably good country with cheap flights back to visit?

Getting control of your financial and personal life may be worth the ticket prices. Your wife's behavior reminds me of human traffickers.