Fish why would a single bloke go out with a woman with a young baby? Because he thinks she is desperate and easy and will be waiting at home while he is out living his life?
I think you're very sensitive about the potential 'motivation' of any man who might (seem to) like you. You are already very untrusting before you've even met someone. This is, surely, because of having been with an abusive partner and still being in conflict with him over your child. It's completely understandable, but I think maybe going for some sort of counselling might help you.
You aren't being unreasonable to be so careful. BUT, your perspective is a bit coloured by what's happened with one person, I think.
A single man would firstly want to go out with you so he isn't single any more. It's always going to be a single man who approaches you or anybody else (you wouldn't want a man who wasn't single ...).
Why would he entertain the idea of a woman who has a young child? Because he likes her? Because he's a nice guy and doesn't mind and understands that he would be in a position of great responsibility and he's up for it?
Because he likes kids and would like to have some with you too?
It is skewed to think that any guy who likes a woman who happens already to have a child is thinking about how she'll be tied to the home and/or considering abusing her child. That is very out of proportion.
You don't seem at all ready to date anybody, but as say, I think talking to someone like a counsellor might help. I'm not saying at all that you should date - it is nobody's business but yours. Of course you don't have to.
You were asking if it's normal to not want to - I think whatever you want is ok for you. It is really hard to date with a young child, and you might often feel a conflict of loyalty/etc. - or time with your child or the guy being compromised. It isn't that easy. So I think fine if you want to wait.
But I'd say try to talk to someone about how you see things, in the meantime.
Good luck at court : ( xxx