I regularly drive coast to coast to see family. I’m about the same age, but male, and never had a problem. I’m departing next week for just that.
If you or your family has a specific concern, I’m willing to address it, but I don’t think you will have any problems.
A few pointers -
You say the car is in good shape, and I believe you, but depending on your last oil change, you may come due along, say, New Mexico. I’d recommend a fresh one, along with a complete fluid check. Check tire pressure, wiper blades, and lights, too.
For multi-day drives, if your goal is to get there, plan on about 600 miles per day. You can do a bit more in the west where speed limits are higher, but 600 miles is a good days drive. You can do more, but you can get real tired, real fast.
But because it sounds like this might be a one and done sort of thing, I’d suggest stoping at an attraction or two. It’s a big, beautiful country, and there are things to see.
Have good audio entertainment. Satellite radio, iPod on shuffle, or books on tape is best, something you don’t have to fiddle with too much.
Don’t eat at chains, look for a local place. McD’s in CA is the same as in TX. Sometimes it may disappoint, but sometimes you find a place where the food is darn good.
Gas up at truck stops. They have lots of turnover, both in the fuel and the coffee - so they’re fresh. Quick off/on the interstate. They almost all have a small store for munchies and travel related items. Not supermarket prices, but well below 7-11 type stores. Gas prices may not be the cheapest for 20 miles, but they will be below average. Restrooms are clean, because truckers demand it. The chains have phone apps to help you find the closest. I like Pilot/Flying J, but Love’s is OK. T/A is OK, but there aren’t as many.
Join a hotel loyalty program. You will probably earn a free night, maybe two or three I f it’s a round trip. I don’t like chain restraints when traveling, but hotel chains don’t bother me.