Hi Farmgirl.
On the tuition and fees, reminder that the system is not the same in England as it is in Scotland. At least here in Scotland, your daughter would have had to have been resident for at least 3 years not for the purpose of higher education. Not familiar with the rules in England/NI/Wales. You might want to pick a representative university and then look at their financial aid web page - there should be some sort of indication of how they establish residency.
Since she's so young, to me it seems that you might be able to make the argument - assuming Brexit doesn't dump on you - that she wasn't here for the three years (when it's time) for that purpose. Worth a try, all they can say is no if they won't allow you the cheaper in-country fees.
The advice we were given was that as long as a child is in higher education and financially dependent, and a member of your household, they can be considered formally "dependent" for EU status.
https://europa.eu/european-union/index_en has a "help" page where you can email them to ask questions related to free movement and exercising your rights as EU citizens (or dependents of same). They also have country-specific experts who will respond. It takes a few days, but they are thorough.
Good luck with the grand adventure!
