Binoculars are the recommendation in The Backyard Astronomer. But, then, they don't particularly recommend buying a child a telescope either.
Personally, I went with a used 4.5" Orion Dob as the first instrument and I think it was a good choice. Now I have larger instruments _and_ binoculars. Yes, a small Dob isn't great for groups because you have to keep adjusting it. But, like people say, polar aligning an EQ is something to be explained too and you're still going to be moving it regularly manually. Doesn't sound like you are budgeting for a motor mount. I can just see binoculars being an interesting challenge as you try to get _each_ kid to find stuff. "No, look at where my finger is pointing. That one! Are you seeing it, the one I'm pointing at?" And, sure, I can see stuff like Jupiter's Galilean moons, the Orion nebula, a lot of moon detail, etc. with the 10x70s but anybody who tells you it's more fun to recline in a lounge chair, hold your breath and maintain your arms as rigid as possible so things don't move _too_ much should probably have his disdain for small Dobs taken with a grain of salt.