EOTAS doesn’t have to be at home or can include a mixture of provision at home and away from the home. Packages are bespoke to individual needs, whatever is suitable and meets DC’s needs.
I suspect the things you are talking about are aimed at under 16.
You suspect wrong. EOTAS packages, including provision away from the home, can be for all age groups, including in your LA.
It would also be up to us to take her to these places as she won’t travel alone.
Parents can not be compelled to deliver, facilitate or organise any provision in an EOTAS package. Transport and an escort can be provided.
It is irrelevant to your DD anyway, because it is obviously not inappropriate for provision to be made in a school for her, therefore she doesn’t meet the LA threshold for EOTAS. I was just highlighting it is incorrect to think EOTAS = no friends.