Nope. That is not appropriate.
Again, my partner has children. They don’t call me mom. They have a mom. They call me Megan or some funny inside joke nickname now and again. But urging a young impressionable child to call another woman mom is kinda weird. It is a gross overstep of his new wife to encourage it. How about a chat between the adults first?
If my partner's kids wanted to call me mom, I would be flattered, but I am an adult, I don’t need to be validated that way — urging them to do it to the discomfort of their own mother. I know I am mom-like to them and they would come to me when it counts. I am loved and respected the same way they love and respect their biological parents.