A.A.
What similar lives we lead....without daddy so much of the time. I have a 14 month old son and a 3 1/2 year old daughter. Since my daughter was 1 my husband has had a job that makes him work way too many hours, plus, this year he started going back to school for nursing. You know how much of his time we get...not much. Since this has been going on for a while, my daughter is very much a mommy's girl. She's a bit older so that makes a difference and we've been working on daddy time. But she has been use to having me around all the time for everything. I think your sister is right. It's nothing you've done really. Your daughter is just use to having you as her primary care giver, comforter, playmate, companion, etc, etc, etc. So of course, she wants that! I so understand about the joy and freedom that shopping solo brings! lol. Encourage your husband to take your daughter somewhere else while you go to the store. Or just let her stay home with him(cause if she melts down, he's better off at home). If he has to run errands, make it a special daddy/daughter errand. If she cries let him comfort her (might take some crying cause she wants mommy, but she has to learn that Daddy can comfort). Let him put her to bed if he's home. This is all pending he is home and available obviously. She just has to learn that daddy can do all the things mommy can do. With his schedule, it will take time, but if he can put every effort and spare minute into spending time with her she'll learn.
Another thing that I've done to teach my kids that being alone is okay is that they have playtime by themselves for a few minutes everyday. By now my daughter can play or "read" books, etc by herself with no problems for over an hour in her room or some special spot. I put my 14 month old in a playpen with some toys and books for 30-45 minutes everyday too. He learns to play quietly without me, to concentrate on his things, and to manipulate and discover new toys. If you were to start this at 22 months, you'd have to work your way up in time. You could also try a blanket instead of a playpen if you think she'll learn to stay on it and play without coming to find you. It's a great way to get stuff done and teach them to play alone. The blanket method teaches self-control also.
Anyway, that's my 5 cents. I feel for you. And I hope things get better!