Wow. Sorry to hear of this. First and foremost: do NOT sign that thing. Don't put your signature on ANYTHING at this point, I don't care what your attorney says.
In this country, the average guy gets screwed when it comes to divorce. Don't believe all those so called 'studies' which 'show' that a guy's situation improves and the wife's deteriorates after a divorce, that is the exception and not the rule. It is time for you to circle the wagons and protect yourself. This won't hurt the kids and in fact will help. Which is worse for them, seeing that you are providing for them and for yourself or having them see you hanging on by a fingernail?
I agree, do NOT threaten your ex in any way. Down that path lies ruin. Now, something you CAN do: forget 50/50 or 70/30 custody. Go for 100% and use the infidelity (IIRC this is what led to the breakup in the first place) as your reason, I don't care what your attorney says. If he keeps stalling and refusing, fire his ass and hire someone else. Warning: if you go this way, it may be rough and will involve dragging her through the mud. Here's the rationale: she put herself in that position. She has made her bed, she needs to lie in it. That 1/2 of the CC debt? She needs to prove that was done for the support of all concerned (you, her, the kids) of it's all on her. FWIW, I refused to accept any part of my ex's debts and she refused any part of mine; the only thing we had to settle was the mortgage on the house and a small account we used for transferring funds back and forth.
Having come out of the gate HARD, now it's negotiation time. You can agree to a different custody percentage in exchange for a drop in the child custody amount. As long as the ex is working and bringing in $ this won't hurt the kids but will guarantee you a monthly amount you can live on.
Something else to be very wary of: in many settlements there's a clause which says, in effect, that if your income goes up a larger amount must be paid to your ex. I know this because it's in my divorce settlement, the difference is she pays ME, not the other way around. Even though the child support was set way back when her income was very low and it's increased since then I have not exercised that clause because honestly 1) I don't really need it and 2) the amount just wouldn't be worth the aggravation of court time etc.
FWIW, there's not exactly a huge body of info on this, but from what I understand there's a lot of ex-pats in Mexico and countries south who got hit with onerous child support and just chose to disappear. I don't advocate this because I think a man's kids are the most important things he will accomplish. I point this out to show just how bad child support and alimony agreements can get; they go past the point of support and become punishment (which is what your ex is really after BTW).
I really really hope this works out for you. Good luck.