I think 9 months is such a hard age - they can't talk, but they're mobile; you're still shattered, but they have so much energy. It really does get easier!
I also come from an abusive background, as does my DP; you can imagine we've done a lot of work.
Something I find helpful is strategising to yourself how much something matters before you start to do it. So, does it matter if the nappy change takes half an hour? Does it matter if the baby runs around without a nappy on? Does it matter if you give up midway through and run a bath instead? Etc.
Obviously sometimes it does matter - you have to get out right now; the baby is covered in poo, etc. But other times it totally doesn't and it is so much easier on your nerves if you can identify those times and go with the flow. In the grand scheme of things, if your child thinks it's hilarious to crawl away without a nappy, well ... fine. Go put the wet one in the bin, wash your hands, and come back to recapture them.
I always did nappy changes standing up at this stage, btw - much easier! Getting a baby to lie down on its back is a battle not worth fighting IMO. If you let them lean against a low table/sofa and give them something to play with at the same time, it's easier too.
Clothes changes the same. DD is nearly 4 and still thinks it is bloody hilarious to race around naked instead of getting dressed. DP always wants to shout at her, but if I possibly can I just let her crack on and get on with the ironing for a bit. Then she gets bored.
But really, seriously, the major lesson I have learned is to find as many opportunities to tell myself 'this is not important'. I think a lot of us from abusive backgrounds have internalised the idea we need to teach a child to behave.
But a nine month old child is not going to learn to behave. They have no conception that they need to be 'good' for a nappy change and I don't think they have the slightest ability to learn that. They learn social interaction from much simpler, less charged exchanges - like when they pass you something and you smile and pass it back.
The aim is to get the nappy on with the minimum of conflict, not to teach the baby to be 'good' while you do it.