I've done the viator group tours elsewhere (in Singapore and Australia) and had great experience with both, so I would recommend it. I had a small group tour in Australia (my party of 5 + 4 or so other people) and that worked out pretty well. The Singapore one was a bit larger in terms of the group size, and it worked just fine too (but it felt more rushed though). I'm not a huge fan of private tours (more pricey, with no opportunity to meet other travelers, but that's just me. )

Anyway, my family visited Taiwan for the first time this year. We thought we needed to book a tour to get the most of out it, but we ended up not needing it after all. We were staying in downtown Taipei and can get to all the main attractions very easily. Part of the reason we decided not to do the tours ws because we weren't interested in all the destinations in the tour package (I read each of them on viator extensively), and it only make sense for us to book the tours for 1. places we can't easily get to (the case for the blue mountains in Australia) and 2. limited time in singapore (there for literally 2.5 days and so we want to see the major highlights)

Transport in super convenient in Taipei too. But yeah, I think the Viators tours are just fine, if not a little pricey for Taiwan. We managed to see a lot, walked a lot, ate a lot, took public transport to further out places, also cabbed it, and managed to leave with fun and fond memories, so it's great, but I definitely agreed with earlier comment about "5-7 days isn't much time to go "around the island". You will see a few highlights, but you should pick and choose and plan the places you're interested in seeing.

Have fun on your trip with your mom!