If you really love your wife-or are willing to do whatever you can to get your family back (even if you don't love her anymore), I would suggest you have a really honest talk with your ex, and tell her what you are thinking of doing to get your family and your life back. Be honest with her about your motivations for re-instatement and ask her if she is willing to live the lie with you if you are willing to put up with your revulsion to the religion. If she cares for you and your kids she may be willing to, provided you can promise to be faithful to her and VERY discreet about your true religious feelings.
Lying to the religion is one thing. Not telling your kids everything-parents do that all the time. Keeping your in-laws out of your personal business-totally ethical. But you can't go back into the marriage with anything less than the truth between you. She may or may not be willing to do this. The staunch JW in her may not be, but the woman who loved you and bore your children and who has to take care of everything $$$ on her own now may like to have her life back. If she isn't, you haven't lost anything. If she does, you have a chance to have a real life with her and to be your kids dad full time again. Even if she doesn't agree to the marriage, if she sees how far you are willing to go for her, she might ask the inlaws to let up on you a bit. Or may encourage the kids to see you more. Worst case she bad mouths you to other JWs. So what? Their respect has got to be of minimal concern, they can't hurt you any more than they have and it will give them a few moments of fun gloating about the ex-JW. Which they do ANYWAY.
If you do anything less, you won't even respect yourself.
I really encourage you to be fair to yourself and your wife before you go any further with this though. Whatever caused you to be unfaithful was a big crack in your marriage. Can that be resolved? It wasn't just about one woman or about the religion.
I wish you well with your life and your family. I hope it all works out for you-however you do it.