Is that Burlington County, NJ?

(Medford)

The best reputation around is at:
https://www.carverwreed.com/about-us
Carver W Reed, pawn shop in Philly.

I would get accepted appraisals that your homeowners accepts then stop by Reed's and see what they say.

then try a knowledgeable jewelry center as pawn shops will low-ball you. Ask for more than your bottom line but keep in mind they have to make something too when they sell it so you can't ask for full market value. Be prepared to haggle.

she's in an emotional and financial pinch, which is why I'd like to hear about reputable entities to inform her.

You might have to step in for your daughter in an emotional time and do the research yourself.

Here's a good link I went to. This particular link is on diamond cuts but you can go to clarity, carat, color and all things diamond on the full site:

https://4cs.gia.edu/en-us/diamond-cut/