Hi Scott,
I have a suggestion, but can't really recommend anything because I don't know enough about your plans. You say you don't want a "sit in" but let me give you another option. I know from experience that kayaks become part of the family so it is a good idea to think long term.
Have you thought about a folding kayak? They are much more family friendly and tend to be quite stable in open waters. Folders aren't designed for rapids or surf but I view that as a plus. I used to teach canoeing and kayaking and these hold up well to the abuse kids inflict.
The ability to fit in one or two bags also is something I personally like, you don't have to worry about a place to store them, they are happy in a closet. It is a hassle to set them up, but once set up, you can keep them assembled and also transport them the same as a rigid kayak, if you so choose.
As to choosing one, it sounds like you want a tandem. I would go with one of the more conservative boats, they are less expensive, have less performance but this may be a plus. You don't really want a performance boat for the family, you want safety. Here is my take of the crew.
Folbot Greenland II -
www.folbot.com - I own one and really like it, low performance, safe, but we have used it in open ocean in Hawaii, until my wife got scared by a sea turtle. Made here in the US with a lifetime warranty. They mean it, they have replaced things on mine that have gone bad from old age. Very good company to work with
Klepper -
http://www.klepper.com/en/index.php - German, need I say more. Very well built, people have crossed oceans in stock Kleppers. Very expensive. Also look at Long Haul Kayaks -
http://www.longhaulfoldingkayaks.com/ - what may be considered a Klepper clone but thought of by many to be better built, they are less expensive being here in the US
Feathercraft -
www.feathercraft.com - I aspire to get one some day but I'm cut off by the wife, no more kayaks, got enough. They have some folding sit on kayaks that are very well received. The company is very innovative and their ideas are now widely copied, a good sign. Very expensive, but everything I have got from them is worth every penny.
I tend to buy used, people buy with the best intentions and then lose interest and off these kayaks at huge savings. I just saw a 2 man Klepper on Craigslist here for $350 in excellent condition, typically used folders go for about 1/2 the price of new. Oh, one last parting thought, if you do get one, also get buoyancy bags, bags you fill with air and fit in the frame under the decks. If you ever go over, and you will with kids, the kayak rides high and they have less water to bail out.
Rich H
1992 Folbot Greenland II
1990 Nautiraid Raid II
2000 Nautiraid Raid I