So sorry your mom's gone. But glad to hear you're interested in preserving these old reels. I took on a similar project last fall. My uncle had just died, and I digitized a bunch of old family interviews with great and grand-parents, old audio letters of aunts and uncles, a few tracks of my grandfather playing bass with Art Van Damme, and some local KY bluegrass sessions with my uncle on bass and backing vocals. Some were on cassette, some were on reels (and a few were the same brand as yours, Scotch Magnetic Tape "Living Letters"). I used an old cassette deck of mine and my uncle's old reel-to-reel player. Ages ranged from 20 - 40 years old and everything converted just fine. Phew! Well worth the effort.
I still have a stack of unlabeled reels to go through, though. I suspect there's not much of interest on them, but one never knows. Just not sure when I'll get to them.
I'd offer to convert yours, but I'm about to move and won't be able to take my uncle's reel-to-reel player with me (I'm leaving it with his family).
If Heath doesn't chime in, you might try sending him a PM as I have a vague recollection he's in the archiving business (or some such). He may have some tips on treatment of the reels to decrease the likelihood of damage during playback and recording.