There are loads of good (unmarked) trails in La Plagne, but the uplift is annoyingly patchy. There are plenty of lifts which open in the summer, but only on certain days, making it irritatingly complicated to put a day’s riding together.
There is a bus back up from the valley, with bike racks / trailer, but it’s not included on the lift pass. For family-friendly riding, there are some short “skills” type trails around the resort villages which are good and some longer blues which might suit depending on level. Les Arcs has better stuff from this point of view, with some decent greens & blues. Access over the Vanoise is pretty easy (and spectacular) but you can only get Paradiski passes on a weekly or seasonal basis, not for day passes (again, pointlessly annoying!).