Op. There’s a lot going on here. Not just with regards this child and her sleeping, but your feelings/ views on the wider situation. My tuppence worth?
You need to step back from this situation and detach. This is a child who at times (for whatever reason) is finding coming for contact deeply distressing. The thought of a mother strapping her child into a car seat whilst this upset to allow contact has me heartbroken as an FYI. I cannot even contemplate my exh (or me) doing that to any of our children. It sounds pretty horrific. And this Is for the parents to resolve. Not you.
If my ExH happily took out kids under these circumstances, I would think he was a complete waste of space. And I hope he would feel the exact same if I did it to him. I would be working with the co-parent/ childs school/ counsellor to understand what was needed to make this transition easier for this child.
Part of which would be looking at the sleeping arrangements. My partner has younger children than I do. They have their own bedrooms at both their mums/ their dads but still (naturally) will come into their mums beds/ co-sleep. Now, do I want to co-sleep with his children? Not a chance in hell. Do I want to be woken at 4am by one of them sneaking into bed and then kicking for the rest of the morning. Not a chance in hell. But do I understand just how much this helps the children? Of course I do. Do I respect that it helps them to bond with their dad, my partner. Of course I do. And things like this are a huge part of why I decided to not cohabit with him and step back massively during his contact time. His children and him need that time and space to connect, including co-sleeping/ cuddles if needed. I would never judge him/ his exwife or the children for any of this. Or seek to say the answer is the exwife should stop xyz.
The answer here is that the father needs to change his approach. He needs to create a home/ environment where this transition is easier. And co- sleeping could be a huge part of that. Some parents in these situations pop a mattress on the floor of the child’s room. As a compromise. And to allow the partner to sleep in their bed Undisturbed / not be kicked out of the adult bed. The partner in turn needs to be wholly supportive and respect that the child needs this time with their parent.
The sentence that also really worries me? We’re all so upset when contact hasn’t gone ahead. Seriously? Why are you upset? Think about that quite gebuinely. Why? My partner missed some contact during covid (understandably) and he was gutted (also understandably). I couldn’t care less (in the nicest possible way) as it was the right thing for the situation but equally, they’re not my kids. I care about them, I want them to thrive, but my life doesn’t change if I see them/ don’t see them. How many would say that’s uncaring but listen, it’s not.
In so many of these situations, and clearly in yours, emotions / transitions are already tough. If I was your partners ex and I had to send my child for contact the way she has had to, I would find it deeply traumatising. Because it is. For both the child and the mother. You piling in your emotions of being ‘so upset’ on top of this is actually deeply unhelpful. The last thing this situation needs is more emotion. What it needs is the grown ups to take a big step back, not make this about them and ask themselves ‘what does this child need.’
My advice? Do that. Take a big step back and encourage your partner to allow some form of co-sleeping with his child. She needs support, not judgement.
Oh and don’t even think about telling the mum what she needs to do. I would tell you where to go if you thought you had the right to tell me how to parent my child.