OP. Have just sat and read your whole thread. Massive sympathies to you and your dc. Just a few thoughts.
My dc first saw ex at his parents, now at his home. The outcome of the time they spent/spend with him had nothing to do with the location. He can be a miserable bugger or cheerful, fun dad at both places.
As for your dc not wanting to sleepover with him. Definitely ask why. I had this and it turned out that ex didn't leave the landing light on at night (see earlier reference to miserable bugger!!). I suggested they asked him to do so, or they didn't want to stay. He got a night light.
Now, one dc always stays the night, the other when it suits (and me!). This is possible because ex lives fairly close, I know this isn't the case for a lot of people.
Cary's phrase is excellent "whilst not rubbishing their father....don't shield him either." This has been my approach. If they say he did so and so, and they're moaning, I will agree with them if I think they're right. By the same token if it sounds like ex was in the right, I'll tell them this. If they start telling me stuff where ex has been dripping the "I'm the victim" crap into their ears, I address this too. I don't slag him off but I'm not counsel for the defence either.
Time on your own without dc. Hideous at first. Lots of tears, biscuits (by the packet) wallowing. Gradually got used to the idea, now 18 months down the line my "just me" evenings (2) and days (1) per week, are packed out in advance. Took a while because I was so sad at first, wanted to hibernate. Now, it's ok, sometimes great, just my new normal.
Communicating with ex. Every case is different. Mine was the script. Let's be amicable. Then quiet contempt when he came to the house. Then him starting arguments so cue me saying pick up kerbside and only text me. Nasty texts. Normal(ish) texts mainly about dc. Lately ok texts about the dc.
If you can be amicable, great, for the kids. But do what you want. Personally, let rip a bit now (as you have) so he can see the damage, then go Ice Queen. I was accused of being a cold hearted cow. Well, be careful what you wish for. As regards my ex, that is now my default.
All in all, it's a bloody hellish journey at times. Probably like all pp I've howled, ranted, sworn like a navvy, stopped the car because I can't stop crying, wanted to scream.
But I've also laughed, danced, met new people, done new things, seen myself become stronger, observed my amazing dc cope (mostly) with the thing I never wanted for them.
Most importantly I've learnt to rely on myself. I'm still here. Bit bruised and battered, but I coped.