I think whilst reasonable, that you didn’t want to sleep with her given the relationship situation, you probably would be best to accept that the relationship situation also means you won’t be having overnights at the moment.
Certainly not without you both being comfortable with that while the baby is so small.
This is why I am advising that, though it is hard, you need to try really hard to take the emotion out of this situation.
If she is also creating part of this conflict you will certainly not help your child or your relationship with your child by allowing your emotions to also control you.
The emotions need to be dialled right down.
Sometimes you need to just grit your teeth and say and do things (with your relationship with your child in mind) that you don’t think are fair.
This is not just re fathers but in fact most separated parents go through this.
Being separated and coparenting is difficult.
I think Larry is rather naive if he believes solicitors calm things down. Solicitors working in this area commonly report that this is only true if the situation involves very high conflict individuals for whom even the smallest issue stands no chance of being resolved in the child’s interests without the involvement of courts.
Your relationship with your child will not be harmed by a bit of breathing space (maybe a week of NC) from the mother to allow you both to calm down.
Then I suggest that you try to use that time to think through how you can go forward resolving these things together as co parents.
If you try your hardest to keep conflict to a minimum and she doesn’t and it ends up affecting the contact for a period of time then is the time to go to mediation. If she will not engage in mediation then is the time to go to court.
If you jump right in to solicitors letters and court you will make it into a power struggle.