LAs and some school often say alternative provison is the responsibility of the school, but section 19 of the Education Act 1996 means it is ultimately the LA’s responsibility. Though if the EHCP is finalised imminently (and it is sufficient and doesn’t need appealing) then it shouldn’t be necessary at this point, but if you think you might have to appeal the EHCP &/or the LA will breach the timescales and you will need to force their hand to finalise, then it is still worth requesting.
Alternative provision can look like whatever is suitable. There isn’t one way or even one dozen ways it can be provided.
It can start at home with a tutor. By tutor I don’t mean an academic sit down tutor but someone who will undertake child led learning doing whatever DD likes doing. Sensory activities, gaming, baking, crafting, playing with toys, gardening, a company with animals visiting your home, watching TV, looking at magazine (you can get Peppa pig ones), etc. Whatever DD is able to do and would interest her. There possibilities are endless. You can get subscription boxes. Either pre-set ones based on DD’s interests or more personalised ones such as Spectrum Space boxes and LCB Education. It can also include therapeutic provision at home - SALT, OT, some form of MH therapy and physio if necessary.
Then, as DD is gradually able to leave the house, it could include things like soft play or trampolining like you mention but also things like rebound therapy (slightly different to just going to a trampoline park and DD may cope with it better), swimming in a private pool (if a public pool is too much), horse riding, visiting a farm or zoo, museums, cafe, bowling, beach, going to a sensory room… As I said it depends on the individual. Some people have formal AP settings involved, such as a care farm, forest school, gaming AP, sports AP, but not everyone does. It depends on needs.
Going forward with the EHCP, the difference between EOTAS/EOTIS packages and the school providing AP is that there wouldn’t be the association with the school which DD may find traumatic and there wouldn’t be the same pressure to work towards increasing time at school. I also think even if DD is to attend a school in the future, because of her trauma, it won’t be anytime soon, and if DD is to not attend the school, the school shouldn’t be named in section I. Also, if you had direct payments, you would have more control over who worked with DD to make sure they were the right person.