Is it normal that all i want to do is be a parent to my child

Sometimes women take over parenting and undermine the father because they feel that they "own" the child, and use them as a weapon. They exclude the father and manipulate their children to follow suit.

Other times women protect their children from shitty fathers, and do all the grunt work because they simply care more and want what's best for the child.

It is very difficult to say which one this is without knowing the situation intimately.

I honestly can't form much of an opinion without knowing your beliefs. I know I'm what some people would consider horribly biased, but it is what it is.

You didnt include enough information for me to make a judgement on your marriage. Working out yalls differences is the best thing for your daughter even if yall stay divorced

She said she felt trapped in the relationship so I said she can be free

"is it normal that we separated because she won't let me be a parent"

For that, I answered no. I meant it's not normal for her to not let you be a parent. If it was you who initiated the separation, I might go with a yes, because you had rights to contribution in the parenting. But if it was her that separated, then that's definitely not normal.