Generally a person has little or no rights over the step children, not unless you adopted them.
How old is your child? If he's young and still nursing, she can't use that as an excuse to block your parenting. Courts would tell her to express her milk and hand it over at exchanges.
There is no excuse for you to have less than "standard" parenting time. The historical dad time (not that this is fair) has been alternate weekends and an evening overnight in between. If he's under 3 years old the court may prefer somewhat shorter weekends but more frequent visits.
I lived for over two years with a typical dad order in my county... .a three day (72 hours) alternate weekend and a 3 hour evening in between. So I had Friday 6 pm to Monday 6 pm. The good thing about that was that when he started school I basically got him from daycare after School on Friday and he want back to his mother from daycare after school on Monday. Only when there was a Monday holiday did I maybe have to have an in-person exchange with her.
Try to maximize the exchanges at neutral areas such as before/after school or with daycare. The in-person exchanges (mine were at the sheriff's office the first few years) really triggered her to heighten the conflict.
Also, I had to suffer through many false allegations. None ended up as "unfounded", a strong legal term. They ended up as "unsubstantiated", a very typical but mediocre weak conclusion. It wasn't until about 2 years after my divorce was final when I had gone back to seek custody in a Change of Circumstances motion that the court clearly made a statement. In regard to a part of her testimony the decision stated it was "not credible".
During my two year divorce I was stuck as an alternate weekend parent. We settled on Trial Day, I learned later her lawyer had told her she would lose at trial. The custody evaluator was for equal time Shared Parenting but his initial report's recommendation was that if it failed then I should have custody. Well, her entitled behaviors, which included playing games with trades, exchanges and phone calls, gave me ammunition to return to court and seek custody and majority time. She even tried to justify obstructing my planned vacation with our son by saying she wanted Kwanzaa, an event we had never observed before, in court she said she wanted to observe the Jewish holiday Kwanzaa. My lawyer had a field day with that one. She clearly confused Kwanzaa with Hanukkah.
There's a saying sometimes repeated here, The poorly behaving parent seldom gets consequences and the well behaving parent seldom gets credit. The point is that court ignores much of the poor behaviors unless it's really bad... .in the USA often the court will consider incidents only within the past 6 months unless a pattern can be demonstrated.
