When I was first prescribed bifocals, I went with progressive lenses. The glasses were kind of small (because that's how I liked my distance glasses) and I had the same problem most of you are describing. So I returned them and decided to just keep using my distance glasses and buy a pair of prescription reading glasses. (My eyes are different prescriptions, so off-the-shelf reading glasses don't work.) I found it to be a hassle swapping glasses all the time, so I decided to try another pair of progressive lenses. This time I went with a larger lens - circular - and that made a huge difference.
And I also hate tilting my head depending on what I'm looking at, so instead, I slide the glasses up a bit for reading, down low for distance, and mid-range for computer work. The progressive nature of the lenses gives me sort of a trifocal effect without actually buying trifocals. That's good, because neither distance glasses nor reading glasses work well when I'm on the computer, which is most of the day.