I don't think that insurance is a good cost to include in the comparison. In a driverless car world, we imagine that insurance costs will be pretty much a constant per mile traveled -- there are no better or worse drivers -- and probably lower than they are now. And you'll have to pay for them (directly or indirectly) whether you rent or own.
If your costs for the second car are more than $1k in just registration and servicing are more than about $500 a year, that, first, suggests that you're not very cost-conscious today. My car's cost service and registration fees are much less than that. Second, service costs also are basically a per-mile fee -- your car's quality doesn't degrade when it sits in your garage, and you'll pay the service costs of a vehicle you use directly or otherwise.
You didn't mention fuel, but of course again that's essentially per-mile, and costs what it costs regardless of the car ownership model.
That leaves registration, which is a small cost, but would be shared in a shared ownership model.
Now, of course, the actual major expense is the cost of buying the car in the first place, defrayed over the lifetime of the car, minus any price you get for selling it. The big advantage of a car-share service would be that you could share that cost with others. If a driverless car costs $50,000 (and we have no idea how much they would cost), and you use it for only 5 years, then sell it for $20,000, you get $6k per year. In a shared ownership model where you share it with three other people, and the company that you're going through makes about 10% gross margin, you're looking at $2.2k instead of $6k, so yay, savings of $3.8k per year. That's a lot of money.
If, on the other hand, a driverless car costs $30k and can be sold after five years for $15k, then it's $3k per year to own and $1.1k per year to rent, you're saving $1.9k instead $3.8k, and that's still not peanuts, but you suggest that right now you spend more than that for a not-very-highly-used second car. The advantages of owning are considerable.