Thats total BS.
I have 2 step kids ive been raising since 3 & 4, now 7 & 8, and their mother knows im not gonna allow nonsense with her/our kids to get between us.
Now dont get me wrong, i dont discipline her kids, and just offer suggestions, but if she's favoring one, or have a disagreement about them, she knows i clearly have a say in things.
I dont know how long you & your wife have been together, or how you get along, but it sounds like she needs a reminder that her kids are eventually going to be out & gone, and if she cant start being rational, and ruins you two's relationship by continuing to separate her & her kids from you, and being overprotective of YOUR kids & not allow you to make any decisions regarding them, then she's not gonna enjoy loneliness....