mollythedogsmum I've tried to read as much as I can, especially looking out for your posts, but I have missed some!
I think their offer is both generous and controlling and I suspect their motives are not what is best for your dd. Because if it was, they would include other local schools.
What did your dh think of the school? What does your dh think of the offer? I am sorry if I missed that, I did try and look for that answer.
In one sense I would find this would drive a wedge between me and my in-laws and in one sense I would find it very hard to relate to them in future. But the offer they have made may benefit your dd in some way.
The first thing I would do is visit the school with dh but not dd. I would visit on a non-visiting day and try and use my critical powers to see how nurturing and kind, fulfilling etc, the environment is.
I'd then (unless truly alarmed by what I found) go again with dh and dd and maybe your son too to visit on the open day/and/or another general day.
If you dd really want to go there I would either say OK to boarding with a six months review in her mind, or I would explore moving closer to the school.
If I chose to move closer to the school I would rent locally, if you can afford to (maybe rent out your house) and see how it worked. This might mean taking your son out of school to a new school but by not selling your own home you could all move back if wished. I'd also explore a sabbatical from work, if you could afford it.
Make sure you also look round all local schools, either state or fee-paying if you could afford and compare this offer with what you could afford/what dd could attend (scholarship or local state school etc, locally).
I'd see what sort of UK residential (e.g. adventure) holidays or otherwise take unaccompanied kids and send dd on one for a week to see how she got on. All as research.
Despite the apparent kindness of this offer I am afraid I would probably lesson off contact with PILs and I would see this as a genuinely hostile move on their part IMHO.
All of these thoughts are my own and of course I would consult my husband about everything too.
Lastly, I agree with Meeep "The sorts of people who would only give you the fees money for their specific chosen school, are exactly the sorts of people who could choose to pull funding at a later stage for some stupid reason or other."
I would really want some sort of reassurances that this would not be the case, e.g. a trust fund set up for both the children's education.
I find this offer from your PILs really quite alarming and am just grateful my in laws both cannot afford this and would never put me/us in this position.
This is no reflection in boarding schools when chosen specifically because they are right for an individual child, which does not appear to be the case here.