AStravelers said:
Computer mapping program shows about 2350 miles from Tampa to Yellowstone. With very young children, I would suggest you plan on two to three 10 hour travel days to cover significant miles then stop for two nights or more then repeat. The 2 night stop gives a full day w/o travel for everyone to chill out. Yes the 10 hour days are tiring but you have a lot of ground to cover.
What you don't want to do with small children is drive, visit something such as museum or scenic/historic location then drive, park for the night and repeat the next day and the day after and the day after. It is best to spend a few hard days to get somewhere, set up camp and then visit what there is to do there for part of the day. Plan on 3-5 days to enjoy the place you stop at. Be sure to get back to camp by 3-4pm to relax and play at the campground. Adults may enjoy driving, sightseeing, driving, camping for then night and repeat. We did sometimes before we had kids. Kids want a place to relax and play or they get cranky.
Plan on at least a week at Yellowstone, 10 days to 2 weeks is better.
I second most of everything that AStravelers said in the above post. We do not travel with kids, but have three dogs with us, so the slowdowns are similar, but for different reasons. I learned the hard way the first time we drove cross country that it is very difficult on the body, the mind and the attitude when driving long distances without a break. I drove from Cape Coral to Gold Canyon, AZ, taking six days to get there and driving an average of 400 miles per day. By the time we arrived, I was wasted and needed a full three days of doing very little to recover.
When we take our trip this year to the Northwest, we will break it up and spend no more than four days on the road without taking a day off and relaxing. This trip will find us spending three days in Iowa to get repairs to the coach made and visit the Winnebago factory, getting us off the road for two full days. We will then spend a week in Deadwood, SD and take four more days just to get to the Grand Tetons. A week there and two weeks in Yellowstone gives me confidence that we'll see much of what we want to between those two very large and impressive parks. Two more weeks in Glacier and a week in Canada traveling the Icefields Parkway between Banff and Jasper National Parks will peak our trip before heading back home.
The one thing I question, but cannot disagree with that AStravelers stated was having 10 hour travel days. If he is talking about 10 hours total, this will equate to driving 7-8 hours per day and is not too bad. But if he is talking about driving 10 hours per day, this will equate to 14-15 hours per day. Since I do not drive with young children, I cannot say this is wrong, but this will make for very long days and I'm afraid anyone of any age may experience cranky attitudes. Most experienced travelers will tell you about the 3/300 rule. You stop driving after 300 miles or at 3:00PM every day you're on the road. While this is geared more to the older RV'ers and can be modified somewhat depending on your driving ability, this is actually a pretty rule of thumb to go by. My wife and I have found that driving 300-325 miles per day fits our style very well and the one thing we have learned about RV'ing is to never, ever be in a hurry. You're supposed to enjoy your vacation, not endure it. We believe the vacation begins when you pull out of your driveway, not when you get to your first destination. Since you stated that you're flexible regarding the length of your trip, you may wish to plan on taking more time to get to Yellowstone rather than hurrying to get there. But AStravelers idea of long driving days broken up with two days off the road every now and then is a good one if the entire family can handle the long days on the road. We will leave Cape Coral on June 1st and not make it to Yellowstone until June 25th.
Regarding the route from Tampa to Yellowstone: I strongly recommend staying away from I-10 through Louisiana and if you search the forum for driver's experiences on this stretch of road, you'll find I'm not the only one. Most of Louisiana's roads are in bad shape; they simply don't spend the money to keep them up. Since you have to head north sooner or later, I recommend doing it sooner to stay away from these roads. Now, the best way for you take is going to depend on what you want to see and do on your way there. If you want to see New Mexico and Arizona before heading north to Wyoming and Montana, you can take I-40 across the country for as far as you want, picking it up in Tennessee and then taking I-15 from Las Vegas north. If you want the fastest route, most maps will tell you to make your way to Kansas City and then take I-29 to I-90 and take it the rest of the way. This is a pretty good route because it allows you to see the Badlands, Black Hills and Big Horns before you get there, giving you plenty of places to stop and stay for a few days on your way to your final destination. If I didn't have to drive to Moscow, IA as my first destination to have coach repairs made, this is probably the route I would have taken. But there are variations of this also, if you want to take I-70 as far cross country as you can, or I-80. That's the nice thing about the cross country interstate roads; there are plenty to choose from and plenty of things to see on each of them, depending on your interests.
Since you didn't denote how you are traveling; i.e. what kind of RV, it's difficult to provide tips to you on what you should count on, what to do or what to bring with you besides the obvious. As someone else stated, you may wish to utilize the Search function on this forum for various topics. There is a wealth of knowledge on this board.
My best advice or tip I can give you - have fun!