I was a stepmom to my stbx's 3 kids. They were placed with us as teenagers, full time, in an emergency type situation, and lived with us until they went off on their own. He didn't have much visitation with them (while I knew him) for the previous 6 years.
I didn't agree with my stbx's parenting techniques. Punishments didn't fit the crime. He was overly strict. I wasn't arguing with his x, I was arguing with him. But, I felt like it wasn't my place to tell him how to discipline HIS kids, even though they were living in MY house. It was a strange situation. Turns out, all the kids ended up moving out as soon as they were old enough and able just to get away from him. It was a completely dysfunctional household.
My advice to you is to be the best father you can to your step kids. They will need much, much love and attention to get through the ordeal. My step kids thank me for being there for them when their mother disappeared from the picture. And, for being the calm constant in their impressionable lives. They've said I'm more like their mother than their birth mother. Keep the kids' welfare in your mind. Not who's doing what to whom. Be their safety net. Ignore the x's rude comments. as Sarah1014 said today
Don't argue with idiots. They will take you down to their level and then beat you with experience. (thanks Sarah1014)