I'd suggest having a van/truck carry the gear and having a parent drive it. Then the kids can likely use whatever bike they already have. And riding unloaded is generally more fun from a riding perspective than loaded with baggage. Get the kids interested in riding first, then they can expand to the loaded touring later if they choose.
I understand the desire to do it self supported. Bigger accomplishment and all that. Doing it yourself. But the extra cost and hassle and struggle kind of out weigh this.