To highlight a few points from T&S post... .Do get legal consultations from multiple family law attorneys, you need more than a form filter and hand holder. Your Ex will continue to find ways to trip you up and sabotage your parenting, so you need a proactive, experienced and resourceful lawyer. Courts and lawyers prefer settlements but your oppositional (high conflict) case makes such approaches impractical. Expect you will have repeated hearings and trials in the years to come, you need someone who can handle that.
Jumping from one relationship to the next is typical when BPD is a factor. It is good that you will require a DNA test to confirm you are father, not that you're avoiding child support but that you need to know you do have rights as father. Don't let her claim you're doing this to avoid CS, don't be described wrongly as a deadbeat dad.
My court has a parenting guideline listing sample parenting schedules. Years later I found out those schedules didn't have any teeth, the magistrates weren't required to use them. However, if you have something like that in your domestic relations court, use it to the maximum for leverage if nothing else. My court listed a schedule for children under 3 years old that assigned the non-primary parent relatively short but frequent visits. I think it was 3-5 visits every two weeks with at least one of them a longer weekend with overnights. So for babies and toddlers visits get to be every 2 to 3 days. So your temp order is unrealistically restrictive.
Understand a real risk with our cases, that our temp orders last much longer than typical. My temp order lasted nearly 2 years and neither lawyers nor magistrate nor judge were inclined to make changes to it, after all, it was just a 'temp' order. That's why you need to get the best temp order or modification you can as soon as possible. It's an uphill struggle to improve it later. I think the judicial perspective is "don't change it if it works".
Is one reason your Ex is getting so much time because she claims she is breastfeeding? That claim is so weak that it's ridiculous. There are ways nursing mothers can express their milk and send it along at exchanges. That has been done by millions of mothers over the decades, both working mothers as well as separated/divorced mothers.
Or is she claiming you're a bad person? That doesn't surprise us here since that is a typical perspective pwBPD have since they see all ended relationships as abusive ones and so those people are blacklisted. Understand that most courts will investigate such claims with a matter of weeks or a couple months and then reassess things once the evaluations are in. Courts will need a reason to greatly limit a father's visitation. Typical reasons are that the children are at risk of substantive child abuse, child endangerment or child neglect. 'Substantive' does not include father overslept, father didn't prepare a meal as mother demanded, mother and father don't agree and similar issues. Essentially, if it is not 'actionable' then it isn't 'substantive'.
She doesn't want me to have any time with our daughter.
If you have a solid, proactive defense and presentation in court then that won't happen. My Ex had that emotional claim but eventually the court decided otherwise. Short term her claims may have caused the court to side with the claimed 'victim' or 'target'. But once the quick evaluations come back that you're not a risk to the child then the court ought adjust the order to typical dad visit schedules — or have their toes held to the metaphorical fire if they don't. A truism often expressed here is that generally you will get a less unfair order from a court than a deal from the disordered Ex .
Does she have a legal history of taking her ended relationships to court such as filing allegations? Is this her first child?