You're asking for a lot. With that budget, you'll most likely be limited to older wood vessels. Also, leaning towards a more dedicated fishing platform (sedan convertible or express) lends itself to less privacy because of the aft deck/cockpit. The above is a generalization; we have a liveaboard on our dock on a 53' Navigator that does just find with a cockpit configuration.
Depending on how old the children are, I believe you'd best be served with an aft cabin vessel with 3 cabin, at least 45' long. Get a small fishing boat that doubles as a tender (we have a 13' Whaler for that purpose).
Peter- Marine Insurance Guru & tuna fishing addict!
1989 52' PT Overseas yachtfisher