I've done Interrail (pre-kids) and I have kids, so I might be able to offer some advice/info.
First, The Man In Seat 61 website is excellent for route planning and guides to rail routes.
Second, longer train rides are more doable on the continent because of the train designs, they're built more for comfort. Especially Switzerland/Austria, they tend to have trains with compartments which means you've got more space to wriggle. Honestly I would 100% recommend Switzerland on trains. You will spend the whole travel time in Switzerland just looking out of the window at the incredible views.
The Italian trains were a bit run down compared to other European countries but largely on time.
If you take lots for your children to do on the trains you'll be able to go for longer journeys per day. I'd recommend doing 1 travel day for up to 6 hours, then taking 2-3 days of not travelling and just exploring a location (even the locations that no one goes on holiday to can be really interesting).
I'd also recommend not relying on devices as plugs can be tricky on some routes (as can phone signal), but take books/paper-based/mini-board-games for the trains.
Screenshot any contact details for hotels, train timetables, map routes etc so you don't need an internet connection just in case it drops at an awkward moment.
Another thing to bear in mind is whatever luggage you take, you'll have to carry it from the train to your hotel and back again, and if you're doing some exploring you'll have to carry it around town, too. I took a backpack but if I did it again I'd take a wheeled carry on case. I strongly recommend you travel as light as possible and definitely keep it to one bag each (plus your handbag) and be sure each of you can pull or carry your own bag because the hardest thing about Interrail is dragging your bags around.
You also need to get your ticket validated to use some routes and reserve a seat before you get on the train. I fell foul of this in Italy and had to pay a €47 fine instead of the €8 it would have been to reserve properly. It's always worth double checking at the station, especially if you have a long journey ahead of you, but most trains I caught were just hop on/off.
On the topic of packing, take one outfit that will keep you warm, one that will keep you cool, one you can swim in, and the rest something in between as most trains and hotels are air conditioned. It can get very cold at altitude even in the height of summer and it can get unbearably hot as you get further south.
If you find yourself in a town and short of accommodation, most Tourist Information centres in Europe can find you a room for the night. I didn't pre-book anything but probably could have saved a lot of money if I had.
The only place I couldn't find a room for the night was Paris which I recommend you avoid. If I could do Interrail again I'd go straight to Brussels then down through Germany, Switzerland, Milan, and across to Venice then on into Eastern Europe. I did most of that route but I wasted loads of time in France due to Paris and I really didn't rate it.
Also grab some nice snacks for each travel day from the local Eurospar or other supermarket, as most trains do drinks but not all trains have a great selection of food. I think the meal I hated most was "currywurst" in Germany. It was the only thing on the menu and it was utterly dismal.
Good luck if you decide to do this adventure!