According to Dugie :

I have a remote car door control, and a piece of the plastic case has been
snapped off. The piece has one of the key-ring loops at the top. The other
loop is on the undamaged half of the case.

After Googling a lot, I still don't know how to identify the type of
plastic, and how make a solid repair. Using "Ambroid ProWeld Professional
Plastic Welder, For styrene, Butyrate, ABS & Acrylic (Lucite or Plexiglas)"
the parts are together now, but not very securely.

Many of these things are made with ABS, but I think the Ambroid
should have worked then. Could have been poor application or
stale glue. Or a different plastic altogether.

Touch a spot on the inside with nail polish or acetone. If the
plastic softens, _fresh_ airplane glue or the ambroid should work.
I've had extremely good success on ABS housings with ABS pipe
glue.

You could hedge your bets with a PVC/ABS transition plumbing
glue. But the ambroid should have been roughly equivalent to that...

Many plastics can't be solvent welded (eg: polyethylene). These
are the plastics that feel slippery and (usually) somewhat softer
than the rigid plastics. You can thermal weld many, but not all
of them. I've not had much success with it either. Practise a lot
first. The trick is slow heat to ensure that the _whole_ bonding
surface softens.

There are some plastics that are just plain difficult to bond
with anything. Eg: except for some unusual situations, once
a delrin or nylon part is broken, it stays broken.

Working from the inside so it looks ok, would hot glue gun material work?

A high temp glue gun might do just enough thermal weld plus "backing" to
work.
--
Chris Lewis,

Age and Treachery will Triumph over Youth and Skill
It's not just anyone who gets a Starship Cruiser class named after them.