No one (including the OP) has said the father should disappear and never see her again, I have no idea how you got that or that she should fuck off.
The father is very involved in his daughter's life, has her 50:50 and pays CMS which he technically shouldn't given he has the child 50%, and on top of all that they end up having the girl even more than 50% when the mother needs help.
The issue here is OPs DP is NOT in a relationship with the mother of his child, it was a one night stand that resulted in a child and he stood up and took responsibility which is great. She has to respect that their relationship is solely about be child simple. The one night stand was 5 years ago, the child is now 4 and the woman is already in another relationship same as DP so the only thing that ties them together is the child.
What people are asking for is boundaries, she does not get to harass DP, send text messages that are not urgent then start chasing and calling demanding that he must respond quickly, calling at midnight for non issues that are not emergencies, suggesting to DP and OP that they shouldn't have children because her daughter likes being a single child, trying to entangle DP I to her relationship issues because she thinks her current partner is cheating etc.
No one at all and said DP should abandon his daughter but you, maybe you're projecting or something but I have absolutely no idea where you got that from.
She needs to respect the fact the DP is in a relationship with OP and their only connection is looking after the child that's it, and if she continues to push boundaries then they can make things official in court, put restrictions in place so any communication is only via email like people do when ex spouses can't stand each other. She has it good now and is being very ridiculous by disrespecting DP's boundaries and relationship.
They are NOT in a relationship, they were NEVER in a relationship and yes there should be mutual respect between them for the sake of the child but she needs to respect their boundaries, yes if there is something urgent then yes call for immediate response but not mundane texts then badgering him for a quick response or calling at midnight.
She shouldn’t have had unprotected sex with HIM if she didn’t want to be a single mother!! and he shouldn't have unprotected sex with HER if he didn't want to be a single dad co-parenting with the mother of HIS child.
The bolded above was a direct response to post below but you've deliberately taken it out of context without the post OP responded to by trying to act like she is blaming the woman for having unprotected sex with a one night stand, she wasn't, both her DP and the woman were responsible and DP has stood up to his responsibility to be a father to the child.
"He obviously didn't mind if she grew him a child or he wouldn't have had unprotected sex with a stranger."
She is not entitled to a relationship with DP, he is not even her ex, and she comes across as needy and obsessed with him. He has no business with what is going on in her relationship.