I'm getting the feeling after reading your sitch that some scripting for you may help you to work out what you need to say to H. I know when I'm in these situations, that nothing seems to come to mind about what i can say. Feel free to ignore any or all of what I've said below, but it's just to gets the grey matter moving about structuring a conversation with H.
If you are going to cancel Friday with him you need to do it tonight! Tell him, you felt uncomfortable on Saturday, list the reasons.
tell him spending sat together was very hard and it made you anxious and feel bad. it's not healthy or normal for a separated couple to hang out all day long. the reason you are separated is because you realise that you aren't able to communicate properly or to have a proper friendship due to all the fights, so it's time to be mature and realise that it's better for both of you to give each other time to get over all the hurt from the last 17years (or you can just say the last couple of years if you prefer).
This conversation will then probably turn into a bigger discussion, where you can bring up that you want to maintain a mature and friendly relationship with him but you aren't able to be buddies with him for quite some time while you get over all the anger and hurt. (turn it around to benefit him). Say it's not fair on him that you are still snappy and grumpy with him and you both need a decent amount of time apart- except for picking up and dropping of d- in order be able to set a good example for d.
tell him you hope he can respect your needs for some space to stop being hurt and angry and to give you space. but that it's still important to you that he puts a lot of time into ensuring his r/s with d stays strong. (you could throw in there about once she hits teenage years it will be harder to connect- so ensuring there's a strong bond now will help that).
bring up friday and tell him You've been looking forward to Friday for so long and you want it to be without any anxiety or worries and you think seeing as he doesn't love the band anyway (and therefore won't be into it as much as you), that you'd prefer he didn't come along (yes this will hurt- think "like a bandaid- like a bandaid!").
If he asks are you taking someone else, say, I haven't planned for that yet. I wanted to ensure that you were ok with not going. Maybe I will try and find someone but for now I wanted to make sure you could understand that this was important to me to do by myself (say 'by myself' rather than saying 'without you').
if he says who is looking after d, then say well there are two choices depending on the outcome of this conversation. if H respects your decision and he doesn't have plans for friday then he can look after her or you can get a babysitter. but he needs to let know by tomorrow morning if he can take her otherwise you will organise a babysitter.
think of all his usual comebacks and have a response for them and then go back to your "script". try not to go around in circles.
hope you don't mind me posting all this. but i know if i'm confused if someone writes something like this it helps me clear my thoughts. also not promising that I haven't written anything that will make him angry.. but hey sounds like he may have to get angry and hurt in order for you to move on. if you like what ive said i suggest cutting and pasting what I've said into word and limiting yourself to a 20min edit time and then call him! Don't chicken out.
it'll be hard but it will get easier if you stand up for yourself now... just like the ad "you're worth it!"