What Op is quite rightly correct about is not introducing the other woman so soon. And that IS for the best interest of the child.
A few people have said that. Legally speaking, this is entirely overridden by the fact that seeing both parents is in the best interest of the child.
It is is possible for the court to decide that meeting other partners very quickly is causing detriment to the child to the extent that it may be preferable for the child to not see one parent. There is a high burden of proof before the court will order that a parent cannot introduce new partners until they've been present for X months, or are living together, etc. Usually there needs to be a pattern of new partners being introduced and then disappearing, and evidence that the child appears to be suffering because of this - repeatedly asking after old partners, for example.
As there is just over half a working day before the contact is due, it's in OP's best interests to come to terms with her current legal position. That is that, unless there is evidence of behaviour that would cause serious concerns about his ability to parent, he could take her to court to get split residency. That would mean OP was legally bound to hand the child over for contact at the frequency set by the court, and it's unlikely she could place conditions on where this contact was or who could be present. Because the child is young, there could possibly be conditions on overnight stays, but these would expire as the child grew up.
She could bank on him not wanting to see his child but it doesn't sound like that is likely.
It's difficult, but OP understandably lashed out at the OW. As she called her a bad mum, it's understandable that OW lashed out back. They were never, realistically, going to be friends at this point. It doesn't mean that the OW will hurt her child. It doesn't suggest she's a child abuser.
If OP were asking me for legal advice, I'd advise that she made clear plans about when he will collect the child and where from, and when and where he'll return the child, ideally in written form. Text is fine. I'd then advise her to be contactable during that period but to also try to distract herself.
If the child comes back with evidence of not having been looked after adequately or having been hurt, that would require further legal advice (and careful collection of evidence, ideally by a neutral party such as the police). But we're not there yet. There's no grounds to be kicking up a fuss. Ideally he'd agree that it's too soon for new partners and see the child on his own, which is what he seems to have suggested that will happen, but OP is a long way from being able to legally order that and by taking that route, risks having to faciitate contact more often than they might be able to negotiate on their own at the moment.