Another place just off the motorway is the Splash Zone at Gullivers World.
As the name suggests it's a watery place - but no actual pool, just lots of splashy things. There's also a small soft play area with a mickey mouse clubhouse theme within it. Not worth going to for the soft play area by itself but your 6 month old might enjoy it more than the splash area or want a bit of both. Not sure if the water side of things means that it will be nice and refreshing or an additional hassle to contend with!
Approx £6 per child and £3 per adult.
<you didn't hear it from me but...> At Westcroft which is just off the M1 too (much closer than 360), there is a large shop complex with a big Tesco and various other bits and bobs. Including a decent MacDonalds which is one of the newly redone ones with interactive tables, fun displays everywhere, lots of ipads to use while you are eating (or once you've finished!) and even a small soft play area and one of those interactive games that is projected onto the floor.
If you want somewhere quick and easy to eat where the kids can also burn off energy, with easy parking, that's it. There's also an M&S in the complex that has a cafe and food department if that's preferable, the Tesco has a cafe and think there might be a Dominos and another place to eat too.
Depends what time you will be stopping by, but there's also a big gymnastics centre just behind Tesco's, that has some open softplay times - might be worth looking at to see if it fits in with your timings... Much cheaper than 360 et al - £4.10 for a parent and toddler, £2.75 for the under 1s. And then just a short wander to grab food nearby if you need it. Probably worth ringing up to ask about if the 6 year old could join in - maybe say she's good at playing with little ones!
Final place is one to remember for the summer (they've turned the inside bit into a gym!) as it is mostly outdoors now - Activity Land
We have a journey from Kent to Derbyshire in a few weeks with a 6yr old dd and a 6 month old ds. My ds is not too good with car journeys so we want to stop somewhere he can have a roll around and a play and my dd can let off some steam!
I think around Milton Keynes is roughly half way so we are looking for somewhere that doesn't require a big diversion from the M1.