Hmm - You don't mention it but I really hope that you're not planning on living on this boat WHILE you are going to med school. As an interlude it sounds like fun - but once you start to study and really need to get involved in things - it is not an option. Most likely outcome is that you'll barely pass, if at all - and be known as the intern who smells funny and has mouldy clothes.
As far as 15K for a boat under 30 feet with standing headroom for 6' + and twin keels - DOESN'T EXIST ! If you find it - then leave the wife and child on shore, pay up your life insurance, and then venture out to sea- it's not fair to drown them as well.
Here's a suggestion...buy a decent Alberg 30 and live on it for a year with the family, making forays up and down the coast. When you start school, move ashore, and apply yourself to your education, for the good of yourself, your wife, your child, and your patients.
Don't set up a huge number of needless obstacles to success, because if you finish medical school properly - you'll be able to buy and fit out whatever boat your heart desires and spend your life sailing and working all over the world.
Don't screw up the long term possibility for a short-term adventure.