"A gulet is an all wooden motor sailing yacht built for cruising the coasts in the calm warm waters of the Mediterranean. These yachts are built to center life on deck during the charter. Spacious decks and housing a large (usually) aft half mooned shaped dining and lounging area are their main features.
A gulet can best be compared to a small hotel afloat. There are double berths in each cabin and occasionally, upper bunks. Every cabin has its and shower. The crew sleeps and uses the facilities in their separate
Common quarters include a large saloon, a fully equipped galley commanded by a cook, lots of uncluttered deck space, sun mattresses strewn all over to laze on while tanning. Round sterned gulets have a mattress covered perch in the aft that is called a "pigeon's nest", the most comfortable place to lounge or nap on the boat, protected by awnings. Unlike a bareboat, which is often limited in water supply, a gulet offers the chance to wash off the salt after every swimming party, as it takes up to 3 tons of fresh water."
Gulet's have a good reputation but a 20M size is not for singlehanding. Nor is taking it on an oceans voyage. You're going to need crew. And a crew of 3 probably won't be enough if problems arise. While I applaud you're wanting to take your family (and they seem to want to be a part of the adventrure) you need crew who have done the trip.
The good thing is that you can get your sea legs in the Med before deciding how to take her home. That may determine the crew complement, time, and outfitting. The complexity of the systems on board can influence the crew size.
If you're going offshore then I'd be leery. If you're going to coastal cruise, then I'd be a bit more agreeable to the passage but I'm still concerned about the original design of this vessel in unprotected waters. Lesser seaworthy vessels have made voyages as long or longer. IMO, the odds of success aren't as good for "calm water designed" boats as they are for coastal or offshore vessels.
And, please, turn the CAPS off. There's no need to yell.