First of all, let me assure you that your children will figure out the truth in due time without anyone having to tell them anything. They are not stupid nor blind; they may not say anything right now, but they are not oblivious.
As for turning the kids against you, your actions will stop that. As long as you continue to be a good, loving, involved parent, your kids will not believe you are a bad mother. They will be confused, because what they see is a good mom and dad is saying otherwise, but I don't think they'll follow his "logic" blindly. When they say something like dad says you're stealing his money, make light of it. If my boss saw me not working (even just coming back from the restroom) he would make a joke about me "stealing" from him. So, just kind of laugh and tell them you're not stealing the money; dad is paying his court-ordered support but just like paying taxes, he feels like he's being robbed" and let it go. The less of a deal you make out of it, the most comfortable your kids will be in talking to you. Of course, you will probably have to go to your room and scream into your pillow, but that's okay. It's not about you, it's about the kids.
I think you could possibly open the door for discussions that involve the other woman by saying something kind of nice about her (I noticed when I called that X has such a nice voice on the phone; or if DD has a new outfit or whatever say something like why don't you wear Y so X can see how nice you look in it. Just something that let's them know that you are not angry at her and don't hate her and it's okay to talk about her in front of you.
If you open up that door and then don't make a big deal out of anything that ex-idiot has to say, your kids will feel a lot less anxious and dad's words will not be able to turn them against you. They will know him as the idiot he is!