Three girls, ages 9, 7, and 6. They are used to sharing.
Three children pushes you very likely into a 3 cabin boat. That pushes you into a 40+ foot boat. Unless you are swimming in money, that means you will likely be looking at a production boat - Catalina, Bene, Jeauneau, Hunter. The exception would be a Catamaran. That would give you the space you need, but that comes with considerable tradeoffs too - the least of which is not cost.
I have a Catalina 400 (as you may well have figured out). It does offer a 3 cabin model, but I am not blown away by the layout. The better layout would be a Catalina 42 three cabin. I guess if the kids were really used to sleeping together, and you got a two cabin, you could put them into queen aft berth and you and the misses take the V berth. I am just trying to figure out how you are going to arrage the sleeping arrangements. A Quarter berth is probably the equivalent of between a full and single sized bed. Can you stick three girls in there and would they be happy?
Another option would be to have one of the kids (probably the oldest) sleep in the salon while two slept in the quarter and you and the wife took the V. Only you can say if that would be practical for your family. It would be difficult for mine as my wife and I generally stay up later than the kids, and often get up earlier.
A 38+ foot production boat from Catalina, Bene, or Jeaunea would have no problem in your cruising grounds. They are there currently and have mad emuch larger ventures. They do have tradeoffs. Other boats of consideration might be something like a Passport 40 or a Tayana 42. My parents own a Tayana 42. I like the boat and it would serve you well - but you would HAVE to put one child in the salon.
If I was in your shoes, and I had to pick a baot and was focused on going cruising, I would probably get a two cabin boat. I would put the kids in the queen berth aft where they could all have a bed and as much room as possible (under the circumstances). That way you and the wife could sit up at night and get up early. There are a variety of boats that would work for you. I would not choose either J or Sabre. I like the older Benes, some of the Jeauneaus, and certainly the Catalinas. We will take our 400 to those cruising grounds, so I am not telling you to do something I would not do. We also lived aboard on a Catalina 380 which would fit your budget better. The negative (and positive) of the 380 is that it has one head. The 400 and 42 have two heads. The 400 is by far the best performing boat.
Others know other boats better. Just make sure you really consider the reality of being stuck on 40ish feet (with your kids) and how that will work day-day. You need room - period. They like their toys, they like to spread out, and they like to argue. They need a way and place to get away from each other. Make sure that as you take opinions on this board, you consider whether those that give it do in fact HAVE kids and HAVE done some serious cruising or LA with them. It is TOTALLY different than two consenting adults... I gotta tell ya.
SO, my choices would be: Catalina 400 or Catalina 42 (both MKii). If the money would not work for one of those, I would opt for a Catalina 380 which is built on a Morgan hull and is more like a tank. She does not perform nearly a well - honestly, but does well in a blow which you will get from time/time. I would avoid the typical blue water type boats because of the tighter space, cockpit arrangements, cost, and sleeping arrangements taht are typical of these types of boats. I would also make sure before I set out on this venture that I made SURE I had a pretty good buy-in from the other four members (ALL your girls). You don't want a mutiny at sea!!
Feel free to ask questions. I woudl be happy to help. I think you are in Texas? ANytime you are up near the DFW area, me and the family have our boat on Lake Texoma. You are welcome to bring your family and see what we have done to make it work and talk about our experiences. You can also view both Catalina 400 (I think I can get you on a Catalina 42), most likely a Hunter 43 (maybe not the best choice but for comparrison), and mom and dad's Tayana 42 which is but a few slips down. You are welcome to look at a Valiant 42 also, but that will be out of your price range and I do not believe it would be the best boat for your purpose.
PS My Catalina 400 has certainly held its value if not increased... even in these times. That is a pretty strong statement given the economy. I think it is because of the technical editor though!!! HEHE!!!
Also, here are some pics of the boat (sorry about the pillow in the floor.... kids, what can I say??)
This was how we split the V berth to seperate out the kids and give them their own space...