There are plenty of problems with step moms who overstep their boundaries with their step child and who make a difficult situation worse.
Your ego has NO PLACE in the situation you find yourself in. You got involved with a man who has a history that involves his children from a previous marriage/relationship. You clearly chose to be in this position.
The children come first.
This does not mean they are more important than your relationship with your partner, it simply means that life gives us a list of priorities. Parents the world over manage to make their relationship important while tending to the number one priority of their children. It is an 18 year commitment, at the least, and it does not change just because you change partners mid stream. You can be part of the team but you cannot show up with your own boat and kidnap the children.
Forget about fighting anyone. Forget about a competition. There is only one intended winner in this and that is the child. The child can only win if everyone realizes they are on the same team.
No badmouthing the mom. No trying to replace the mom. No keeping the child from the mom – EVER. If you are going to pursue these practices then you are committing child abuse. You look up Parental Alienation Syndrome and get ready because the courts are finally recognizing it and starting to hold the offenders accountable. Even if you escape legal consequences, the children will eventually hold you accountable. You will have to live with the knowledge you destroyed a child with your petty hate and anger. It is not a legacy that is easy to live with as you go gentle into the final years of your life.
If your happiness depends on knowing that you have forced a mother to go to bed sobbing for her child, then you have a serious problem. And you need help.
The following articles are insightful and helpful in encouraging people to work together and do the right thing for the children.