We do pretty much that drive every few months... The nicest (NT) place to stop is Barrington Court - lovely gardens and the best cream teas for miles, and acres of lawn for running around on. It's a bit close to the Bath end tbh (we stop there on the way back, mostly) but it's the best.
To be honest, depending how old your children are and what needs they have, I wouldn't stop at all if you can avoid it.
We have done a similar run a few times (we're very near Bath), and it's been very quick. It's nearly always a really good run and we've never needed a stop-off, so stopping would only prolong the journey.
Unless you just fancy meandering down in your own time and having a stop en-route of course!