For example: Mom takes service to work, possibly carpooling. Dad takes uses family car to drop off kids and goes to work. Car drives itself to mom's work for her to use to pick up kids and commute home. Dad takes service home. Or whatever. The point is kids can always be in the car with the extra diapers, with safety features parents want, etc.
The other part of this that people ignore is that a car sharing service could open up a lot of flexibility. For example, maybe our dedicated family car is just a sedan, but on this particular weekend with the grandparents in town, we can use the car sharing service to get a minivan and have everyone ride together. Or I want to pick up a piece of furniture and request a truck from the service. Or it's my anniversary, and I can request a luxury sedan to drive us to the restaurant for a touch of opulence. I'm sure there are many other examples people can think of.
Like you say, car sharing won't cover everyone's need, especially at first, but eventually, the big players in the space will have enough sophistication to cover many cases, especially for a second car.
Car sharing starts to make sense when you want the car outside of rush hour. Want to go to the store for an hour at 2:30, no problem there are plenty of cars free. Want to get to work every day - you are paying peak rates for a car that will probably be used exactly twice that day, once to get you to work and once to get you home.
(This assumes that you're also from the US, for rhetorical convenience.)
At this point in time, I think it's wise to avoid laying costly new tracks with the dawn of driverless cars on the horizon.
In fact, this is a perfect use case for driverless cars. The problem with trains everywhere is the wasted time not on the train and the million stops along the way.
It gives us exactingly detailed information on what journeys people need. The dataset will be immensely valuable in allowing the companies that sit on them to first start doing quasi-bus services:
Order a bunch of minibuses. During peak hours, offer an option: Wait for the next dedicated car to be free, or ride share with quicker availability and a discount. Limit detours strictly - there'll be plenty of "Follow road X and pick up 6 people on the way to station Y" type stretches that will make people happy (little time lost; feels efficient if there's not lots of turning off).
Then you can see them partnering with bus providers to dynamically fill in during peak hours, or even bidding for bus franchises and proposing contract changes that would allow for more dynamic, demand-based scheduling.
Ultimately this can feed into planning train type services - companies offering these type of drive share will be able to e.g. let people order "end to end" journeys of the type "pick me up at address 1, get me to address 2" where they show journey options that include rail when it makes sense. The key beying that if they do so, they will know the entire desired journey, and would be able to offer insight into the most efficient interchange locations or other changes to train services would be most desirable.
The raving reviews you'd get the first times people order a car and are told instantly "your car is already waiting right outside your door" would be rather interesting.
Get in, and your favorite radio station or music is playing.
And for colder climates: Your car is already pre-heated. I remember too many winter mornings during winter in Norway when even ensuring our car would actually start in the morning was an annoyance (even with a garage, space heaters in the garage or motor heaters is sometimes necessary).
Yes they will; the magic trains you're thinking of are called streetcars. And, with the oddities in oil and the difficulties of maintaining suburbia, we'll be moving back to dense streetcar suburbs soon enough.
We still have typewriters around too, and some people ride horses. Old tech doesn't die, it just diminishes to a smaller niche.
Car seats will be a bigger problem: they are unwieldy, legally mandated, and require careful installation to be effective. Unlike diapers, even the small boosters used for older children can't fit in a shoulder bag.
A young couple expecting to have children in the next few years might balk at these inconveniences, and that could depress adoption of the 'mobility' model. You have to keep prospective purchasers in mind, who are evaluating their needs over the use-life of a car.
I know many people who keep golf clubs in their car because sometimes a salesman is looking to round out a 4-some. I like going to walmart/lowes... over lunch and leaving my treasures in my car.
Car sharing won't actually work out anyway because everyone needs their car during rush hour. Everyone is driving then anyway, and then the cars sit idle.