You poor thing, that sounds so frustrating.

Are there little things you can give Kai to do while you put dd down? Maybe he can quietly "read a book" to her while you feed her?

It may be that he just needs time. Do you think he would respond well to a reward chart?

I'm very much into natural consequences - and I'd probably be explaining to my child who was not being co-operative at bedtime that the more time I had to spend getting dd down, because of the older child playing up, the less time I would have to spend with them at bedtime and that would make us both sad but you can't be up all night getting bedtime done. It might be hairy to start off with, but it seems like a fairly natural consequence to me.