Hello Strestmum.
I can see why you're posting this: In a situation like this you need a range of opinions to bounce your own off, and in so doing, help you to come to some sort of conclusion about the "shape" of the situation and what you might do about it.
Ideally, you'd ask lots of other mothers in the class, who have "seen" what's going on and have an "angle" on it - not just your dd's bf's mum, but you can't, because that might be "gossipping" and you're a nice person and don't want to make anyone feel bad. Hence mumsnet.
Drawback with mn is that we only have your "angle", which is a bit limiting.
Never mind; we'll do our best.
Here is just one possible angle/interpretation - and you can just use it to bounce around - it's not necessarily "right" or "wrong":
Firstly - I would step right back. I would cancel the playdate and actually, I would give some minimal and vague excuse: "dd is tired after school at the moment, let's leave it for now" and I would just take a raincheck with regards to letting them get together at some future date. That buys you time to think about what you're going to do, without having to do anything now, in haste.
Why I would do that has something to do with the following:
Schools are funny places. Kids go there to learn curriculum stuff but actually, the biggest thing they learn is socialisation. For example, they learn that behaviour A will lose you friends and make life hard, while if you adopt behaviour B, life will become radically easier. Hopefully they will learn that people will respond positively and favourably to behaviour you if you move from behaviour A to behaviour B. Kids also learn to be forgiving and tolerant, hopefully.
As adults/parents/carers, we should talk, listen, interpret, offer advice. We should keep a close eye and make sure behaviour doesn't cross lines (eg. bullying, isolating) and intervene (firmly) if it does.
And no - I find it impossible to follow my own advice. I am often quite an overly-interventionist parent!
So, one possible interpretation: Jay arrives. Your dd offers to be her playground buddy. Jay is interesting, intelligent, articulate. Your dd is drawn to her. Jay wants your dd as her one, intense friend. Such intensity is attractive. No doubt it makes your dd feel special, wanted. Jay insists on your dd being her exclusive friend, and adopts quite heavy behaviour if your dd doesn't comply (even these, to my mind, rather un-normal e-mails).
Amazingly, your dd says No.
She has somehow worked out in her head that Jay, for all her good and attractive points, has a rather worrying type of behaviour, that she is uncomfortable with. Despite various adult interventions, Jay is persisting in that type of behaviour. It's not changing. Your dd has decided that, even with all Jay's good points, behaviour A is just too much and she has a choice; accept behaviour A or lose Jay's friendship.
She's chosen to lose Jay's friendship.
Actually, that is quite mature reasoning.
Just think of all those adult women who are still puzzling that one out.
I think at this point, having spoken to the teacher, I would have discussed with my dd what was going on and kept an eye on it to see that things weren't descending into bullying/exclusion. I'd wait to see if Jay cooled down the way she approaches relationships.
I'm not at all sure I would have re-negotiated the re-opening of the friendship, on unchanged terms.
Oddly enough, as parents, we tend to bring an overly-adult perspective in our children's relationships, over-coloured by our own memories of school and our own anxieties about what we want/need our children to be/act out for us.
I think we have to trust our children to be quite good at negotiating this sort of stuff - though obviously with our help. You're obviously a very decent person and motivated by a great deal of generosity. Your dd will surely pick up on that and carry it into her dealings with others. I think you have to trust her a little.
Leave it for a bit - I'd be amazed if Jay doesn't move on and find someone more suitable for a close friendship. Someone who actually really needs a close, one on one friendship. There's certain to be someone in the class who perhaps needs that kind of friendship and will thrive in Jay's company. In a weird way, keeping Jay and your dd together is stopping Jay either finding another friend or learning different "friendship" tactics.
Obviously, if it descends into Jay being isolated or ostracised, I'd go and have another chat with the teacher/review tactics. But, given time, the new-bf scenario is the most likely.
Btw - I was genuinely a bit surprised by the e-mails. I have no idea if that is normal angsty stuff in eight year olds. Also, you are clearly reading your dd's e-mails but is Jay's mum equally interested?
So there we go - just one possible interpretation. I've no idea if it's the right one. I'm only putting one possible slant on the information given. I'm sure there are many others.
Good luck.