Too many cooks in this picture to establish responsibility, not blame,
for the problem, IMHO.
The shop probably "bought" the remanufactured transmission from a
commercial rebuilder and essentially handed it over to you.
You installed it in good faith and followed their instructions to flush
the cooling lines.
After two weeks use it won't shift.
IMHO the answer will be unknown until the problem is fixed (and may
always remain so).
Dirt in the valve body will point the finger at you. A broken part in
the box will point the finger at the rebuilder.
Notice that no finger is pointing at the shop that sold you this box for
your DIY project.
The dispute would be between them and the rebuilder if the shop had
installed the now crippled box; it now appears to be between you and
them, but them only as the rebuilder's sales agent.
The rebuilder probably offers a warranty on the box, most likely with a
condition or two about its installation. That's going to be the
governing language as to who pays - you or the rebuilder. The shop is
only a conduit in this situation so you can't hold them responsible. You
need the shop's help to deal with the rebuilder so don't get into a
dispute with them; they're your reluctant friends here. I say reluctant
because they deal with the rebuilder a lot more than they deal with you
- so where's their loyalty going to be??
In this instance the repair shop is nothing more than a retailer.
Not what you wanted to read but you asked for opinions; that's mine.