I own a 32' monohull, so maybe my comments will be helpful.
We've charted many times in the Caribbean and the BVIs. Early on, only monohulls, usually Bene 44 or 50 or 51.
Lately, we've only done cats, including 45, 49 and 50. Normally the crew consists of 4 couples, all adults. On the monos, usually 3 couples, but sometimes 2 families with kids. Commonly some of the couples have little or no sailing experience.
It's a kick to try the cats for a change, and their accomodations are gigantic compared to monos. In the charter trade they have been killing the monos as charter boats the last few years. There's just all kinds of spread out and have fun room.
In the BVI and most of the Caribbean you will spend little or no time at docks; instead you will either be on a mooring or at
anchor. The additional beam of a cat is inconsequential in those settings. If you aren't comfortable docking at the end of the trip the charter companies invariably will do the docking for you. Some of them insist on taking the helm during docking (we had that experience recently in Martinique, which was OK with us as all the boats were med moored (bow secured to an
anchor, and then backed in with the stern tied to the dock; no finger slips, so everything is congested and there's no room for errror).
The biggest challenge I've had on cats wasn't mentioned above: raising the mainsail can be a very daunting task if there isn't an electric halyard, or a means of using the
anchor windlass to power the mainsail halyard (several cats use that method), or a couple of strong guys. Mainsails on the bigger cats can br enormous.
The mainsail on my 32' mono is about 250 square feet; on the bigger cats the mainsails are well over 1100 square feet, and built of heavier fabric. I've never seen one that didn't use full battens. They are heavy sails.
I can raise the main on my boat without a
winch for all but the last foot or so of tightening. On the 50' cat we chartered a few months ago the main was raised by something like a 2 speed
Lewmar 58 mounted at the base of the mast. We needed the highest gear ratio for the last 10-15 feet of hoist, and the lower gear for all the rest of the lift.
It can also be troublesome to keep the full battens out of the
lazyjacks because the mast is so tall that raising the main takes some time. Two crew to raise the main is useful on some of the bigger cats.
If you are sailing just with your family, I wouldn't go any larger than a cat in the 37-38' range. It will have probably triple the space of your 30' mono. It won't heel much, if at all (most of the cats don't even have
fiddles on the counters). The area on the trampoline up front is a great place while sailing or while anchored. The cockpits usually have large dining tables, which is were everyone wants to eat in the evenings.
You should have a great time.
On the cruising cats, the experience really isn't anything at all like the beach cats/Hobies. They are a bit quicker than monos, but not shockingly so (because they aren't as weatherly the extra speed while beating doesn't translate to a whole lot better VMG; on a reach they will sail quite a bit faster than a mono). They don't fly a hull, at least not with me driving.
As someone else said, the first few tacks can be a learning experience. You ease through the tack in a big wide arc; don't throw the helm over quickly.
Reef early because you don't have an increasing heeling angle to tell you the boat is overpowered. If the boat has wind instruments you will be advised by the charter company about the maximum wind speeds they want you to sail in before reefing.
In general, your sailing skills will transfer pretty easily.
My wife won't even consider any charter besides a cat anymore.
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Having said that, cruising size multihulls are very, very difficult to capsize as a general rule. 
