It's feasible. As one would expect, it depends a lot on your flying comfort level, what type of accommodation you're after and what you're planning on doing while over there, really. I'm currently just putting the finishing touches on a 3 week trip over there this summer, with myself, DH, and DDs aged 16 and 12.
Our flights were ~£5k + several years of airline points accumulation. That's in Premium Economy with a large British carrier. If you're happy in economy with a Chinese airline that can take the shorter route over Russian airspace, you should be able to get cheaper flights. Especially if you book as soon as the tickets release.
Our accommodation has clocked in at ~£5k, excluding the few nights at Tokyo Disney. However, we are mostly staying at Mimaru apartments so we have a bit more space, the kids can have their own room, we have laundry facilities to reduce the number of clothes we need to take, and we can make our own meals to keep food costs down. If you're happy all sharing a room in a small hotel in a less central area, or risking an AirBnB, you should be able to bring accommodation in cheaper.
Entertainment costs are very variable. From £0 to have an official guided tour of the inner gardens of the Imperial Palace, to £20-£60 to visit Osaka Castle, go up the Sky Building or visit TeamLabs, to £80-£400 for private experience classes such as mochi pounding or a cookery lesson. (Rough prices are for four people, not each!) Plan out your itinerary and book tickets early, as popular attractions can and do sell out quickly.
We're not doing Universal Studios, but saying on site and going to both the Disney parks over 2 days is an eyewatering ~£1.5k. However that's mostly the accommodation. If you're happy staying off site and travelling in, then park tickets for 4 people for 2 days (1 park per day) is ~£200