Any reasonable judge will not hold your being on ADs against you. If anything, your lawyer can position it as you are doing the RESPONSIBLE thing to make sure you are caring well for your children, and then can give concrete examples of how you are there for them, and contrast with your record-keeping of husband's poor attempts at same.
His adulterous behavior may not come to bear in the divorce action itself, due to the "no-fault" state in which you live, but it will probably come to bear in the alimony, and it will DEFINITELY come to bear in the custody. I am in Florida, also a no-fault state, and this is how my attorney described it to me.
Also, if you are not already doing so, be SURE to keep records of the money he is spending on the hotel rooms and anything else that is associated with their affair. Ask your attorney about "dissipation of marital assets" -- I think your husband is on very shaky ground here.
Any time my wife tried to talk to me about divorce or separation or threats along those lines, I merely said "Now that this is a legal matter, that's for the attorneys to decide," and I refused to get into it with her. I constantly reminded her that I did NOT want a divorce, and that I was willing to work at our marriage, but that I would not begin that until she ended her affair -- PERIOD. And once the D was actually filed, anything "legal" I would defer to our attorneys. It's just not worth the aggravation to get into it with them, at best, and at WORST you may end up doing/saying something they can use against you.
You're on good, solid ground -- keep doing what you're doing, and don't let him push your buttons. It sounds like he's very good at it, but you're getting better at not responding. That's good!!!!