My advice is to try and reduce the number of variables you are trying to solve for.
Which in your case means ignoring the younger child for now. She will be living with you; you are likely to end up in a college town of sort-- the local public schools in these towns tend to be very, very good. So no need to contort yourself to figure out a plan which meets both kids needs AND has them in the same place AND can be/might be affordable, with music for the elder child and who knows what for the younger child…
Re: the older child- why the interest in boarding at all if you all end up in the US at the same time? I understand it as a fallback if your timing is delayed… but if you all end up in the same place and you find an easy and convenient day program for her- wouldn’t that be optimal?
I’m a little uncomfortable with the “we can make it work” strategy unless you actually HAVE the cash in hand for their education (and four years each of college- which is no joke financially). And I don’t know how an educational institute is going to factor in having a parent who is a full time doctoral student regarding aid.
My head is spinning. But the more information you give us the better we can advise you.