I had my gallbladder out a couple of years ago when I was 22. This was a few years before I was dxed with CML. I laid in bed for a couple of days and then found strength to gingerly get around. Recovery for me was fine, and I pushed myself to drive back to school sooner than I should have, but it wasn't too bad.
I was tired for the week after the surgery but I didn't have any problems with nausea. Just eat like they tell you at first so that you can ease your digestive system into it.
Otherwise I can't give any insight on how things are with TKIs, but all in all there are worse surgeries!