The problem with your request isn't that it is unreasonable it's that you can't explain what "right" feels like to you, and you can't explain what "not right" feels like, you've just emphasized how you think it feels but not how it is different. So how are we supposed to know or figure it out?

One concern I have is that you said you needed new tires, and you used a mechanic to tell you that... How many miles were on that tire? I'm going to guess at least 40,000 km? Blistering is a heat condition. Have you been drifting in your car? I would never call a normally driven tire "blistered" because it's common only in track vehicles with extreme tire slip. Wet cobblestone roads can cause blistering, so I'm guessing you might have had that for a lot of miles.

Worn tires and bad alignment might be the norm fo you, so a new tire, wheel balance and alignment might clear up the "wobbly" back end.