You also shop more often, and you get the children to help carry bags! You can wear a backpack and put a lot in that, and have a couple of decent size cloth carriers to get loads in. If you cycle, you have baskets and panniers, and backpacks.
You can use Streetcar, where you hire a car by the hour, and you can go to the non-central supermarkets where there are car parks.
Or, as acekicker said, online delivery.
Students also make noise, just perhaps at slightly different times.
But the accommodation that St John's will find for you would be suitable for families, and not mixed in with students, likely. It would be a small house somewhere near the college, most likely.
If you want loads of space and bathrooms in the house, you will need to be very rich, and/or live way out in a village somewhere. Not in the centre. And that would be a real shame, missed opportunity to learn a lot about another culture, especially for the children.
Remember too that it's not just that the island is small and crowded, and that some of these things are necessary for that reason - but also, that people actively choose to live this way. I remember some Americans at college who didn't adapt very well, because they couldn't ever get over the idea that we would all have the lifestyle they were used to if we could, and that while they were accepting of the fact that it might be too expensive/crowded to have that here, a few of them were a bit patronising and still gave off the attitude that people would want it if they could. They didn't realise that lots of people actually liked being in the centre of it all, having lots of little shops etc, the environmental benefits of cycling/walking, the cosiness of small older houses, the feeling of not being wasteful with resources/space/money, the huge number of cultural opportunities in very close proximity, the diversity, the liberal views, etc etc. It wasn't just that people were "making do" here because they couldn't have what the Americans were used to. The students who appreciated that got on much better. I was from north america myself. There were things from home that I missed and many things that I had to change my views on. In the end, I liked it so much I stayed. It was clear to me that people were choosing to be here, and that in their view, it was likely as good as or even better than what I was used to, and I wanted to be able to see it that way - so that's what I made the effort to do. And here I still am, many years later.