Guess, if it were me I'd do or consider a couple things...
1. Have ford dealer or trusted service shop check transmission fluid, and give me their opinion on it making the trip. Maybe add a transmission temp gauge if you don't have one equipped now.
2. Consider whether now is the time to upgrade the truck? Maybe your looking for an excuse to get a newer eco-boost?
If you drive it and the transmission fails, do like you say and rent a truck for the rest of the trip. Life is too short and kids grow too fast to worry about this stuff though. Your right about this being important for your 7yo. I was able to take my 7 and 5 year old DD's two years ago, but that was before owning a camper so we flew and rode the busses! Great time, great memories, great CC billss.....But sooo worth it!
One quick story..I used to have a 97 suburban that drove great, shifted fine, but felt a little looseish at times. Always worried about the transmission going out at a bad time. On a tent camping trip with a couple friends, one of my buddies older "camping truck's" wouldn't start. I pulled him 6 miles into the nearest town as we didn't think a service guy would be able to find the truck where we were camping. Pulled him fine and all seemed well, until I unhooked from him and went to back up....No reverse, no park! Arghh. All forward gears still worked fine, and so was able to haul both my buddies and get us all home. $2500 for a rebuilt tranny with 3 yrs of warranty and then I wasn't so scared to tow. Bought a new burb and then our old 28BH TT and decided the camper was an excuse for a real truck. Now I have a F250 and since I could pull more, now we have a 5er...
Like I said, no use worrying, but I get what your saying.
Good Luck and ENJOY the Trip!