I can't comment on your thoughts about the other school - but I can comment on the home ed worries you have.
For what is worth - you are not alone in your concerns - I think they are common to most people before the try HE. Things to remember - HE doesn't have to be a long term decision - but it might be the right decision for your DD at the moment - to give her a chance to recover from the current situation - and by the sound of it she does need to recover. HE doesn' have to be a once and forever decision - it can be the best decision at one point, and then school is a better one at another stage - you can move between the two as appropriate.
1)I would be no good at it, I would fail to give DD a decent education. I am counteracting this with the fact she is learning very little currently so anything will be an improvement.
It is not a case of teaching so much as facilitating. You provide the opportunities for her to learn in a way that suits her - I am sure you can do that in the short term at least - most people can handle primary school level stuff - just give her opportunities to explore, read, play with numbers and measurements etc
2) socialisation
This is always a concern - but it doesn't need to be. You can keep in touch with school friends, join after school clubs, and if you want to go to HE groups - there is more to socialising than being in a classroom.
3) Finances.
It doesn't have to cost much in terms of equipment and trips - but like everything - you can spend a lot if you want to. Your biggest cost would be lack of earnings - again something that is likely to evolve over time.
4)Someone said to me today, 'you can't home ed, you would never get any time to yourself' I really don't know what to say to this one. would i go crazy at home everyday with DD ( and possibly DS too) ? i don't know but during holidays i love spending time with them and I always feel a bit sad when they go back to school. i guess that's one that only time will tell but I'm sure I can arrange for DD to go out for a day or 2 with other people if needed. Likewise if she needed more time away from me.
You find space for yourselves - you and the children. They are less stressed, and often more able to entertain (and educate) themselves - they don't need constant input from you. Again - it is a try it and see situation - everyone finds what works for them, and that may change over time.
FWIW - I would go with sick leave for immediate effect, with a serious thought about options - which may include current school, other school, some other school or HE.