Here are the low down on the rides...considering that you want to pick your first "family" ride...oooo I can't see the options again so I'll try to remember...
Space Mountain...the cars for space mountain seat three, in single file, with one person in each section, there is a chance that your DD4 could fit with your DS10 in one section, or with a parent with not too long legs. Otherwise, your first family ride will be in two separate cars, and keep in mind that you will not be visually sharing the experience, like looking at your kids face as they ride their first ride in WDW.
Buzz Lightyear...the cars for this ride could seat three across, if the third is relatively small. We fit, DH, DS6, and me, and each one of us had a control. The two outside sitters had the guns, and the middle sitter did the joystick. So, same goes here, you will be in two separate cars for this ride. That said, you spin around in the cars and you could easily share the experience with each other as in various points during the ride there is not too much activity. This was my DS6 first ride in WDW and he loved loved loved it.

We hit it early in the morning on an am EMH, and we rode it quickly 3X in a row, with each of us taking a turn in each position.
Indy...the cars are two per car for this ride. So again, not a shared experience, and you are so far apart in the cars that you don't really have much contact. The ride is fun, especially if the kids drive. DS kept yelling to make it go faster though, so a little low on the thrill factor in that way.
Pirates...You would all be able to fit in this car. You would have a shared ride experience...especially if your DS10 is a fan, this would be a really fun ride to go on together. It is a classic ride, and one that you don't easily forget, it has a lot to look at, and it is entertaining, and somewhat tame as well, with just a couple of dips. This ride does NOT offer FP, so if you hit this ride first thing, you would have the best shot of having the shortest wait for it. That is assuming that you are planning on hitting MK at rope drop.
Splash Mountain...This is another ride that you would be able to ride altogether in. I don't know that you would all fit in one row, but you would all be in the same car. It is a similar ride experience to Pirates with a lot to look at as you float along the river. Of course, this one is more of a thrill with the decent at the end. And you would run the risk of getting wet first thing in the morning, unless you took precautions (wearing a parka or something), and you may not want that.
I voted for Splash Mountain because you seemed to be wanting a more family experience and I think Splash is the closest to that. A main draw back to that is the fact that a lot of people head there first thing and so you may be looking at a wait first thing to ride your first ride...and I don't know if you care about that. FP is available for Splash, but then that would imply that you would go ride something else in the meantime.
I don't know if this helps you in your decision/planning...but I hope it does! I hope you have a wonderful vacation to the World!
