Do step-parents have any rights?

If my BD gets married, what things can they now do? For example can she participate in exchanges like pick up the kids without him? Also, if he’s not home with the kids and I know it can I just go pick them up because they’re home alone with her? Our court papers give us each the right of first refusal so if we aren’t going to be around our kids, we have to ask the other person if they want the kids before we can get an outside babysitter. If he’s not home why would I want my kids around just her?

Added: I’ve always had problems with this woman interfering with our coparenting ever since she got with my ex (while I was pregnant I might add). My ex and I used to just talk; he’d call when he wanted the kids but she pushed him into taking me to court, now I only have my kids half the week and I miss them. If he’s not with them, they should be with me. That’s not being petty; simply a Mom loving her kids.