My car overheated. had to replace upper radiator hose. Now car shakes when idling and transmission changes gears hard. Advance auto ran a check and it showed codes p0770, 0113, 0171, 0174, 0301, 0302, 0303, 0306, 0313. more concerned with the hard shifting than the codes re: possible spark plug firing issues.
There are 2 unrelated issues going on here. The poor idling may well reflect a blown headgasket from the overheating event you mention. This would show up as rough idling and spark plug firing issues/codes.
The harsh shifting can be the result of higher-mileage wear, or the failure of a shift solenoid. The shift solenoid adapts to your individual transmission, and your driving behavior.
For the potential blown headgasket issue, I would recommend having the engine’s shaking inspected by a mobile, professional mechanic, such as one from YourMechanic, to diagnose this problem, get an accurate assessment of damage and cost estimate for repairs.
For the transmission issue - disconnect your battery for 20+ minutes, reconnect, then drive around for 15-20 minutes as you would normally. The transmission will revert to default shift parameters, and "re-learn" shifting. If that exercise does not correct the harsh shifting, take your car to a reputable transmission shop for a thorough diagnosis.