While he may be close with his parents, he MUST realize that he is NOT blameless in this situation. I mean, for Pete's sakes, he CHEATED on you, and he wasn't honest about financial issues that affected you -- those are HUGE issues that would shake any marriage to it's core!! Many marriages just wouldn't survive it.
So if you two have talked this out cooly and calmly and decided that this is the best solution for the time being, then I applaud you for it rather than making a mad dash for the court system and getting a divorce.
As for your Anxiety disorder, who WOULDN'T have one after having dealt with his cheating and the financial secrets?? That would throw anyone into a tailspin -- and now you don't know if you can trust him anymore.
His family needs to keep their noses OUT of your marriage/issues and let you two work things out! And HE needs to tell them to stay OUT of it. If he's not man enough to do that, then you might be in trouble if he's THAT close to them. You might want to remind him not to discuss ANY of your problems with them, as everything is PRIVATE and not to be shared with them under any circumstances. If he needs someone to talk to, go see a therapist, but don't talk to the family about it!
I hope this all works out for you. You two DO sound like you're committed to one another and I hope this time apart leads back to getting together again. I wish you the very best! Please keep us posted. God bless and take care. Hugs, Lee