A two inch hole sounds big to me. I think mine is only slight larger than an inch. I had to work the stems gently through the holes, but didn't want to see the soil falling out without having to use filler. The filler I planned to use, if it was necessary was newspaper.
I am not seeing harm from the wind of my plants. Maybe your plants were weakened by something else? Are you fertilizing them? Was there residue in the bucket before you planted? Are you over watering? Maybe bone meal and egg shells will strengthen them? I also shake the stem a little bit - heard someone say it encourages pollination from the bees. It does seem to release the tomato scent. But that could be my imagination. I've been doing it when the main stem is as fat as my finger - I think it stimulates the circulation for stronger main stem.
Because tomatoes can be sensitive about too much sun, and gusts of wind, maybe you can try a spot where they will get a little bit of shelter or shade?
I'm not sure what else to suggest. I haven't been doing a lot of fussing with mine. I do talk to them a lot and spend time making them feel like famous stars taking their photos. I've brushed against them quite often with no damage. I'm no expert, but am planning to setup a few more of my tomato plants now that the first are doing well. I'd be interested in your solutions in case I run into problems. I love my tomatoes and it fills me with fear to think of losing them.
"Love all God's creatures, the animals, the plants. Love everything to perceive the divine mystery in all." -Fyodor Dostoyevsky