I'm no expert on whale shark viewing and I'll let others respond to that. Suffice to say that I believe most trips are two day affairs to increase your chances of seeing one. If you plan a one-day trip you may or may not be successful. But TCR have recently run such trips and they can report how successful they were.
If you look at the maps at
Belize Maps, Ambergris Caye, San Pedro, Caribbean and Central American Maps it'll be clear that TCR is closer to all three atolls than is AC. Particularly so for Turneffe and Glovers (which latter is for all practical purposes inaccessible from AC), less so for Lighthouse. By "a day away" I mean a fairly early start and a return too late to do much else that day. 8am-4pm would count. If I remember correctly our outing to Lighthouse started a little before 8am and ended at dusk, around 6pm. But it was a very relaxed day, while by no stretch of the imagination can that day trip from AC be called "relaxing", regardless of which operator you choose. Of course, we didn't do the BH dive (because no-one wanted to do it) so that reduced time pressures considerably. It was lovely stopping at a rocky headland for our home-made lunch, and having time to dawdle and gaze at the creatures in the rock pools.
I did a few day trips from TCR, but really there's no limit. The mainland sites to the north, such as Altun Ha, would be a struggle but there are alternatives, at least equivalent and debatably better, which are well within reach. I've been to Caves Branch (all sorts of activities there) and to Mayan ruins at Xunantunich and Cahal Pech, with stops along the way at markets in Belmopan and San Ignacio and at a wonderful farm shop between Belmopan and Dangriga. All so much easier because you're on TCR's own minibus and (within reason) they go where and when you want, as if you were driving your own car but without the associated hassles. Informal yet effective. They also do trips to the south, but I haven't sampled those.
To be fair, TCR's island neighbour Coco Plum Resort runs similar trips in much the same way.
