Re education: I'm pretty sure Meghan is going to make sure Lilibet goes to the LA girls' private school that she didn't get into, and will be THAT mom who makes sure hers is the most sought after playdate and party etc. She'll avenge her own snubs and inferiorities through her daughter.
Gwyneth Paltrow went to a school in Manhattan that my own DD regularly competes against in one of her extra-curriculars. It's a girls' private school unlike any UK girls' private school I know of. The closest equivalent would be St Pauls, I guess, but the small size of the school, immense wealth, super-tiny and exclusive social circles and zero even lip-service paid to a broad and diverse student pool really has no comparator in the UK. Maybe Eton, for boys, but Eton isn't as universally revered amongst the types of families that would consider it as this school is. This school (and there are one or two for boys, and a couple of next-tier ones for girls) is off the charts for exclusivity, which is cultivated by faculty, staff, parents and, most distastefully of all, the girls. They live and breathe it, it's their raison d'etre. It's actually pretty gross to see in action. I can well and truly believe that GP is the original nepo baby mean girl as some parts of the press (which haven't been scrubbed by her PR) would have you believe. Apple doesn't seem to have fallen far from the tree, just grafted onto the SoCal scene.
That world and Apple Martin's path in LA is what MM will want for her DD. Hell will freeze over before she gives up having "arrived" (via her daughter) in the world she couldn't penetrate as a child herself, in favour of Marlborough or Wellington or wherever Charlotte is/will be at school. Such a school would also serve no purpose for MM. That world isn't relevant to Meghan or her aspirations for her daughter. And it's all about her, as we know. For all her global recognition and fame/infamy, Meghan Markle is actually extremely narrow-minded and uncomfortable outside the tiny world of monied Southern California, and a small group of ever-changing people in it (probably because she needs to be top dog at all times, difficult to do in a big arena).
The American and British school systems are also poles apart. Neither Harry nor Meghan strike me as having high academic aspirations for their children, and your DC have to have a fair level of aptitude to transition between the two. Mostly, though, the idea of sending your children off to school a 14hr+ journey away from LA, when you have perfectly decent and indeed coveted schools right there, where the world's uber-celebrities send their children with more in-built securidee infrastructure than you could shake a stick at, and where you can keep control over their every day social lives, is preposterous. If you're familiar with both worlds, it's obvious that school in the UK for Lilibet (other than maybe a year abroad to give her royal-adjacent kudos) just wouldn't happen. Especially not when her mom's on record talking about handing As Ever over to her as a thriving business!
Note nothing about Archie here because, frankly, the poor boy barely gets a look in as far as him mom goes and she's the only one posting on SM about her DC.