Hello,
Having a baby during PhD bring a lot of challenges but that is not the problem.
I got a nice supervisor before but couldn't stay after my pregnancy. When I got back from parental leave I got a new supervisor. He is a nice person, new in the university, no power yet, so wants to do everything very well as everyone at beginning of a new job.
The problem is that I need to compromise in something (baby or PhD), therefore I am not pursuing the greatest thesis anymore, I only want to submit a thesis. But my new supervisor is demanding and wants extra tests that I do not consider necessary for answering the research question. This gives me a lot of extra work. I Tried to speak with him but he let me very clear that not following his "advice" is like offending him. Even threat me to give up being my supervisor or to complain of my choices during defence.
I am in the final year and have few work missing to complete my thesis (that I was highly motivated to do it before). But I think that he wants to have more contribution on it, as good as he can, because I am his first PhD at the University. Extra to this I think that he feels threatened by my cosupervisor that is expert in the topic but can't be the main supervisor by the internal rules.
It seems that everything the supervisor does is very well done and following the rules but I am getting unexpected work that give no gain (management things also) giving me a lot of frustration and delaying the PhD.
I know what to do and how to do to it in my thesis work (my previous supervisor and cosupervisor also thinks that is a valuable research) but I need my main supervisor "signature" to finish. How can I make it easier without compromise my baby?

Be honest with him and tell him that you don't like his supervision technique. You are a new mother and your concerns are legitimate so don't fell that you are in the wrong. If he is new he will want a PhD completion and you asking for a new supervisor will look good for him at all. So if you say that you want a new supervisor unless he is more supportive you might gain traction.

What does your co-supervisor say? Does he agree with the new one about the extra work?

My Co supervisor is working in other institution and I only going to be with him in a month. I am afraid of confront him once that with him it can back fire. He is doing well, you know. He said that we should take as much as we can even that we already have answer to the question. I think that he sees me as a lazy person because I do not want to do it. He do not understand that I want to do take as much as I can of the time that I have with my baby as a baby and not of a thesis. I will have a talk with my Co supervisor to see if I can handle it in the most soft way.

I take it he doesn't have kids and maybe doesn't understand how much work they can be. Just drop hints about how much work the baby is, how it is affecting your sleep and you desperately want to finish to get a real job. He might just not realise how life changing a baby is.