Hello!

Just had my car serviced for a dozen different things, i'll list them incase it's relevant:
Transaxle oil pan gasket, replaced
stabilizer bar control link replaced
transaxle case cover gasket, replaced
Differential output seal, replaced
tightened an alternator belt
new spark plugs

transmission fluid and filter changed too

After all this, I leave the shop, 15 minutes down the road my check engine light comes on. I stop to check fluids(only thing i know how to do) and find the trasmission fluid is a tad high.

Further down the way, I stop at a light. Try to go again, but it wont let me get past 30mph, refusing to shift higher(2nd or 3rd gear?). Park, turn off engine, and restart. Go and its fine.. until i hit another light. It repeats until i turn off and restart my car.

I take it back into the shop the next day to check THAT out and they get the codes from it
P0700 and p1776
They called a transmission shop for me, and they suggestion a full overhaul, rebuilding it. That seems rather extreme!

Googling the codes myself though, it doesnt sound like it needs quite that much work. I wonder if i'm being taken for a ride.

What i've come across suggests replacing the solenoid pack and/or valve body.

Real question here is, does that require a transmission shop or can a general mechanic do it. I dont want to take it to a transmission shop if i can help it. Though i certainly cant do the work myself.

Any advice would be appreciated
Also, should the mechanic that serviced my car be responsible for these new repairs?