Please help...

That may sound a bit harsh. But, there`s a populist view that if you work with your parents to let them know you can patch things up and live happily ever after with your partner, then it might change the situation. This is a modern day fallacy- in most cases. Maybe your parents think that you wont be compatible enough or they might think that the girl might not be ready with the kind of situation she`s in right now since your married with your ex and have kids. Nevertheless, if you really love her, you must fight for it and show them that this is the girl that I wanna spend my whole life with. The girl should also do her part to let your parents know how much she loves you.

First of all, you ruined any normal relationship by meeting this girl while you were still with your wife. I assume that is the case, no? But if your only worry is to please your mother, try to get your girlfriend to do things that may please her and try to let your mom see the good things about your girlfriend. In the end, if you mom still doesn't like her, then there's no point in worrying over it. If that guilt consumes you, then you'd probably be best without the girlfriend, because you can't have a healthy relationship with nightmares from your mom. But if you can live with your mom not liking her, then no worries, move forth.