If your flights aren't locked in yet, consider "open jaw" (multi-city) flights, from home to London and back home from Edinburgh or Glasgow (which might involve a London connection). This may come out costing less, or no more, than your four fares on the overnight train. And give you a better sleep that night -- unless the overnight train is something you want to experience for itself.
If you do that, you'll want to drive from London to Bath to York to Edinburgh instead of the reverse. Either way, Via Michelin can help you plan and schedule the road trip -- with the caveat that it commonly underestimates actual drive times, which must allow for traffic and necessary stops. Assuming that you drive south as you now plan to, it shows about 4 1/2 hours from Edinburgh to York, which would give you time for a detour to Hadrian's Wall and maybe even Durham Cathedral. But those stops would eat up time you could otherwise spend sightseeing in York itself.
The drive from York to Bath is about the same 4 1/2 hours. I haven't done it, so I don't know what sights might be easy stops, except for Gloucester Cathedral. But you may need that morning for York sightseeing if you didn't get there early enough the day before. If you choose Oxford instead of Bath the drive will be somewhat shorter.
From Bath to London's western suburbs is a couple of hours, giving you some morning time in Bath. From Oxford it should be a shorter drive. You may want to drive straight to Heathrow and spend the night there before your flight.
For me, this would be a very rushed itinerary -- not only the road trip, but the short stays in London and Edinburgh. Realizing that your spring break time is limited, I'd still suggest you give yourselves fewer stops and more time in each. Consider the open-jaw suggestion above, with a car or train from London to York, then driving to Edinburgh, then flying home from there or Glasgow. That would give you a couple of nights in York with a full day's sightseeing there, and let you make other stops along that more direct route. Bath will cost you time you might better spend elsewhere, experiencing more than Britain's excellent motorways.
