Changing location of litter box (long)

Since my husband and I are expecting babies (twins) soon, I wanted to move our cat's litterbox out of the kitchen and into the garage. We put swinging cat doors in all the doors she will need to use and spent a few weeks trying to get her to go through them. We started by sitting on either side of the door and passing our 1 1/2 year old kitty back and forth through the cat door. We praised her and spent some time petting her for encouragement whenever she stepped through on her own. After a few days of this, we would put her one the other side of the door from us and her food and would wait patiently for her to come back through on her own. After a few hours, she would always do so. However, we have been unable to figure out how to get her to go from "our side" to the other side on her own. She doesn't like treats, so putting one on the other side won't help.

As the birth of our babies got closer, we decided to just try moving the litter box and see how she did. We made sure to show her where it was (just on the other side of the garage door) and encouraged her to go through her cat door to get to it. I expected a few accidents, but hoped she would quickly catch on. For the first few nights, my husband passed her through her cat door into the garage and she would use her box. But, as soon as he stopped, she refused to go to the garage on her own. Instead she has pooped on our carpet and on the couch. Each time we realized she had done this, we immediately passed her through to the garage. She always comes back out on her own after a few hours or less, but she still refuses to go in on her own.

What can I do to help her? Did I miss a step along the way or do I just have to keep doing this until she finally gets it right?

Either she doesn't like to be alone in the garage or she doesn't like going through the cat door. Did she ever get hurt by it? Like her tail getting caught or the door suddenly swinging back on her nose?
If nothing like that happened, try leaving it open for a few days. Put the box in the kitchen side near the open cat door. Let her use her litterbox for maybe a couple of days. Then transfer the box to the garage placing it again near the open cat door. When she is comfortable going back and forth to use the box, put down the flap of the cat door and see how she reacts. If she is used to going through, I don't think she'll mind the swinging flap. Good luck!