To answer your initial question. Yes. If I wanted a particular caliber, and finances were not an issue, I wouldn't let the fact that I had a similar one prevent me from buying it.
There is little difference in the .280, .30-06 & .308. With the bullet weights that are available for each you should be able to find a load sufficient for both you and the grandchildren. Given that you already have a .308, it would be cheaper to buy the .308 dies and work with that caliber. I'm not sure they exist, but you may look for some managed recoil loads for the .308.
The .243 is a great cartridge and can offer lower recoil for the grandchildren. You mention the .280, .30-06 and .308. Does the .243 meet your needs in a big game caliber?
If you are all set to buy a new rifle, there are a lot of options with the calibers you mention. I would go with what would be the most cost effective and serve your needs.