Body shop returned car in worse condition but won’t take accountability

I am in a bit of a strange situation. I was hit (not at fault) and went through the other driver’s insurance for repairs. The body shop kept delaying my car even after I told them multiple times I was leaving the country on Feb 27 and needed it before then. They ended up finishing it March 4. Because of the delays and the fact they wouldn’t keep the car, they drove it themselves to a parking garage while I was out of the country instead of offering to store it at their lot.

When I got the car back, it honestly looked worse than before. The front bumper is sagging, panel gaps are off, and there are parts that aren’t even secured (there’s trim near the windshield I can literally lift with my hand). Now I bring the car back and instead of just fixing it, they’re trying to say it must have been hit again in the garage and are telling me to open a new claim.

There is a small scrape on the lower bumper from leaving the garage, but it’s low and cosmetic. I took a turn too wide and scraped a curb but it wasn’t enough impact to cause the misalignment currently present. It doesn’t explain the bumper sagging, the gaps, or the loose parts across the front.

The owner of the shop actually took a video of the car after parking it in the garage, and you can already see the gaps in that video. So the issues were clearly there, and they’re still trying to deny it.

I called my insurance (GEICO) and they told me I can’t “double dip” and receive two payments, which I get, but that’s not what I’m trying to do. I just don’t want Progressive to get away with dodging responsibility for a bad repair.

So now I’m stuck wondering:

1) Do I keep pushing Progressive to fix this under the original claim?

2) If I go through GEICO, would they actually go after Progressive if it’s determined the repair wasn’t done correctly?

3) Or am I about to get stuck paying for this somehow? Do I have grounds for legal counsel?

At this point I just want my car fixed correctly and to not get screwed over in the process.