We've rarely had a problem with odors and really don't do anything out of the ordinary. Many folks wait until the black tank is about 2/3+ full, however we've always dumped at the end of a weekend camping trip...just because. At that point, I add a dose of Odorlos + about 5 gallons of water. It's been several weeks between our last trip and now, and over the weekend I noticed just a slight odor, so added another bit of Odorlos and some more water. Water is the key to the whole thing. We've never considered solid/liquid as any problem. TP is always just a cheapie, single ply rather than investing in the $$ RV stuff...a waste of money. If you have a tank flusher, great! If not, you might look into a Tornado or similar system. AND spring for a clear fitting so you can actually see what's coming out. Many a time, we've thought the tank was clean and ready, only to flush again and surprise! And never, never leave the tank dry.
Re the black tank treatment...we've used Odorlos for many years with satisfactory results. Many others use the Geo method - you can Google that - and others use different products. A few use no chemicals at all and I'd be hesitant to do that for both odor control and digestion of any solids or paper.
Re the kids, certainly understand that, but I would just make it a habit as you're in and out of the camper, just make a stop by the bathroom and give it a dose of water....maybe a count of 10 or so. Then, even if the kiddos don't add enough water, you'll have done it. Another "mom" job! Water....lots and lots of water.
Agree checking the vents is the start. If all is clear, then you're good. WATER.