Ebbie,
I don't have a PA-28, but I have seen some about like that you depict.
A bit of information might make your situation more easy to understand (so I'm not forming an opinion one way or the other here).
Were the replacement interior parts genuine Piper parts? If so, your issue is probably as much with Piper as with the installer. The installer does not have the right to modify the parts to make them fit, they just install what Piper supplies. If the parts were not Piper, what makes them "airworthy"? Are they PMA parts? If so, again, you may have an issue with the manufacturer as much as the installer.
The installer may just say "we installed the parts approved for the plane". That is their job. If the parts come with provision to adjust to fit, then they should have been. But, my experience has been that some formed plastic interior parts either look nice installed, or don't - there's no provision to "adjust" for a better fit.
My experience has been that most Piper and Cessna had interior finish which was modest at best, Though not great, I've seen factory planes which looked as bad as the photos you present.
Probably, the installer is as frustrated with your lack of satisfaction as you are. You will probably have better luck teaming with them to collectively find a solution, than sitting on opposite side of the table right off. Simply ask them what opportunities they had to do a better job of the installation. If they say "none", they may be telling you the truth....