Podgorica is not a must-see.
Tirana is not a particularly exciting place, but I think if you're going to Theth it makes sense to see at least one Albanian city. At the moment the country's top historical, art and archaeological museums are all closed. The first two are in Tirana and the third is in nearby Durres. That's painful in a country whose relatively few museums are not generally up to European standards in the first place. Tirana was my first experience of having planned too many days in a city, and I'm have traveled a lot. It's not an unpleasant place, but I don't think the concept of zoning has made its way to Albania, and the city is rather thin on sights from my perspective. Two nights would be my recommendation for a traveler with general interests, or 3 nights for people especially interested in Albania's 20th-century experience; the latter would potentially be interested in Bunk'art 1, Bunk'art 2 and the House of Leaves. I will warn you that traffic in Tirana can be really bad; I wouldn't want to drive there.
I'm in Shkoder now. It's much less hectic than Tirana. It has a good museum about the post-war period, the Site of Witness and Memory. Unfortunately, the English translations occasionally seemed wrong, and they didn't appear to have been reviewed by a native speaker. Shkoder is much more convenient to Theth (and Montenegro) than Tirana is, and I wouldn't feel impelled to go to Tirana as long as the key museums are inaccessible. (And not having seen them, I can't comment on their quality.) A day would be plenty of time in Sjkoder for the typical tourist not planning side trips.
My favorite destinations in Albania were Korce, Gjirokaster and Berat, but they're less geographically convenient. On the other hand, distances aren't great, and since you'll be driving, you won't have to deal with the massive frustration involved in obtaining basic bus information on departure points, arrival points and departure times.
I've been in Albania and North Macedonia since mid-May, and it has been hot on most days. You may run into quite unpleasant temperatures when you're not in the mountains or on the water.
Edited to add: Since you're going to be driving, I want to mention that Albania doesn't have a lot of traffic signals but is inordinately fond of traffic circles (roundabouts). Be absolutely sure you are aware of the local rules regarding those. No promises as to whether folks tend to follow whatever the rules are; I haven't been driving. However, I've seen no accidents, so the circles seem to work.
Be sure to notify the rental-car company of your plan to go to Albania. I've read the road to Theft was repaved recently. With luck it will still be in good shape for you next year. On the other hand, the road from Shkoder to Lake Koman is very rough; I think damage to the undercarriage would be possible if the driver didn't go very slowly. I recommend being very careful about your insurance coverage.
Taxis will take you just about anywhere you want to go in Albania, usually for much less than it would cost in points north and west.
