I think one of the difficulties here is that the family do not know what will be best for the dd! The potential to uproot the whole family to a new location, what about her and her dh's jobs, the son's school ect before he joins his sister, or to have their dd living far away from age 11 - this is all massive.
Definitely if it really would benefit her, then being a weekly border seems a reasonable idea.
user1474815709 "If it's a good school, I would move. Sorry but not the time to be selfish if your children are really going to benefit from it."
I don't think there is any suggestion the OP is being selfish! She has a job and another child to consider, as, presumably, does her dh.
"I wouldn't take it as arrogancy on their side but also consider how awkward things can get after you decline."
IMHO I think it is highly arrogant of grandparents to consider they know what is best for their grandchild and to offer this somewhat poison chalice.
I certainly would not worry one jot about their feelings if me and my dh and dd decided to decline the offer. In fact if the dd decided it was not for her I would distance myself from the pils because I could well imagine the offer might then come back for the son in a few years time and the whole business start up again.
My dd is dyslexic and really struggles at school. I was very worried about local school and looked far and wide to see what would work. We could not afford private but some local schools might be better.
In the end we allowed our dd to choose and she chose the local school as all her friends were going, and it has worked out really well and she is very happy.
Being unhappy, even in a good school, may well lead to bad outcomes for a child, a good school is only good if it is good for you (your dd).
I am not sure I think being engaged in school activities from 8.00 am. to 9 pm all week and half days on Saturday, as another poster mentioned, is good at all.