This is last on the list because this is often the area where the skipper must compromise most. If you are devoted to the notion of sailing your boat well and fast and often, in both light air and strong conditions, you run some risk of first boring and then demoralizing your young crew. At least until kids start learning to sail themselves, they will always clamor for the engine to be run and for getting somewhere sooner rather than later when you might prefer to ghost along in zephyrs. And—on monohulls at least—they may well feel very nervous when the boat starts heeling. In all cases characteristics that increase interior volume and livability will also decrease performance.
This is also the one area where catamarans sometimes are not optimal. True, a cat does not heel, and this is always reassuring to children, but optimizing a cat for performance—installing daggerboards instead of shoal keels, narrowing hulls, raising bridgedecks and restricting or eliminating bridgedeck saloons—proportionately steals away more kid-friendly features than is the case with monohulls. On the whole, once you factor in windward performance and especially helm feel, a good cruising cat will be less satisfying to sail than a good cruising monohull.
Monohulls also are generally easier to sail under one sail alone, which increases options in emergencies and also creates more opportunities to keep sailing when you might otherwise stop. Some monohulls will beat to weather under a headsail alone, and many others will sail (upwind and down) under a main alone. Most cats do not have such capabilities.
I’m not saying that you shouldn’t opt for a cruising cat if you can afford one. My general philosophy is that, when cruising with kids in the early stages of their sailing careers, it is far better to take it easy and sail, as it were, with one arm tied behind your back. It can be quite frustrating at times, but reefing earlier and motorsailing more often so as to keep your crew feeling safe and comfortable is usually the percentage move. Cruising cats work very well when sailed this way, as do many monohulls. Otherwise, I strongly recommend you wait until your kids are older, more knowledgeable, and more experienced before you splurge on a performance-oriented boat that you can sail both hard and fast.