Whenever you reach any city destination (and a few others like Gecko mine), you can use the "Town/World" button to go in via an alternate entrance. Hub, for example, has Old Town and Market entrances which are both very convenient.
I updated the wiki page about the Engine Upgrade within minutes of reading your original post here, so now you'll see this:
"To get the upgrade, you don't actually need to bring the vehicle to T-Ray. You only need to bring him the vehicle's Key. "
That was not there before this thread.
And sorry that comedy does not translate well here - i was joking about using the forum to tell people where you're going (because they will wait for you there and kill you lol). Ignore that part i guess. Tell us all everything.
So now...i might have to reverse that edit. The "spare key" option from T-Ray can be done with only a key, and i admit i assumed the engine upgrade works like that too. Sounds like i was wrong. Thanks for reporting it.
However, there is no way I know to get your vehicle into the garage. The only time any vehicles ever are inside the garage is when they first appear as the result of a fresh new purchase. Once driven away, they do not ever again get access to the inside of the garage. T-Ray's dialogue does suggest otherwise - maybe that could be "fixed" some day. So when you go/return there with a vehicle, the vehicle will park outside of the garage. (Maybe that's good enough? I don't know.)
Please do let us know what you find, and i will edit the wiki accordingly.