If everything doesn't fit in the trunk, you can use the car, if you have the room to do so.
The Pride GO-GO travel scooters, which we are getting one are easy to dismantle and assemble. It's been demonstrated that sixth graders are able to do it. This travel scooter will not have a piece that's more than 35 pounds. The wheel base will not be bigger than 42" long and 22" wide and some styles are slightly smaller. I doubt if these are available for rent, but there are many models of Pride scooters. I think you will be looking at the heaviest piece to be about 45 to 50 pounds and slighly bigger.
You can always get the name/brand of the scooter (from the rental place, etc) and do a search on it to see how it's broken down and sizes of the dismantled pieces and how much each piece weighs, etc. You can do the same for most car trunks. This takes a little work to do, but it would give you the most accurate info for what you want to know. The rental places for the car and scooter may have this info, if you ask.
If you are
renting a scooter after you get the rental car, I would simply take the car to the scooter rental place and make sure it works for you. This is probably the simplest way to do it. I would have my trunk empty, if you go direct to the scooter rental. I don't know how convenient this is to do, but it's very safe this way. Usually, the rental place will demonstrate everything for you, too.
Although, it's more expensive you can rent scooters at the Disney parks and other places like SeaWorld, etc., too. Then, you don't have to have it in your car and you don't have to worry about putting it together or charging the battery.