We drive down from WV. It takes around 12 hours for my dh and I to drive it straight through. We do fine, but after driving it, we wouldn't visit the parks on check in days because of the long drive. With the four of you driving, you should be able to split the driving to where it will be pretty manageable. Just try to nap in the car between taking turns.
As far as traveling with another family, I would suggest that the four of you sit down and talk about what your expectations are as far as how much time you are going to spend together. While it's nice to think that you can do everything together, it's also important to have some family alone time too, so I definitely suggest that you all set some boundaries as far as that goes for all of your sanity. Even the best of friends and the closest of families have ventured to Disney together with the expectations that they would spend every waking moment together, only to find that they end up aggravated because of lack of family/alone time.
In addition to that, it's important to also discuss your daily itineraries. Are you early risers? Do they like to sleep in? Do you want to make rope drop? Do they prefer to stay at the parks later? All of these things are important and its best to be flexible because after all, it's everyone's vacation. For instance, if you like an early start, you and your family can head to the parks early and then once they get up and get moving, you can meet up for lunch and then explore the parks together, or vice versa. I know that the point of your family and their family taking the trip together is to spend time together and that is fine, but it's also important to have alone time too, for everyone's sake.
If you are all early risers, then you could head out to the parks together and spend the morning exploring together. Then after lunch, you could split up to have some family time and then meet back up for dinner later. I'm not trying to discourage you, but the key to traveling together with other people is to set aside time for just you and your family.
I just realized that you will all be in the same vehicle and your renting a condo, so coming and going will be a bit harder. However, you can still plan for time to yourselves. It's doable, just plan ahead.