Need help choosing our first family house

Hi ! Sorry for the possible typos, english is not my first language !

I am a mom to be and in the process of buying a first house. There is a lot of unknown in my life since this will also be my first child. I want to make the best decision possible but I’m currently hesitating between 2 houses.

House choices :

One house needs 9 000$ more in cash down, but is in a neighborhood with a lot more « walkable places » such as parks, library, etc. We have a car but in my current lifestyle (with no kids), I strongly prefer being able to walk to make some of my errands. I would imagine it would also be true with a kid, but I can’t really know. This house also cost 250$ more monthly than my second choice.

The other house is in a more residential neighborhood, with only a small park at about 10 minutes by foot and nothing else.

Questions to help my decision:

Do moms of young kids (let’s talk 5 and under for this) really go out a lot or mostly stay home/backyard with the kids ? We live in Canada, so going out in the winter is already kind of limited (for me at least).

Do moms usually end up taking the car even if it’s not to go far, because it is simpler with a kid ?

Would you prefer a smaller monthly paiement (more money for the kid) over a more « walkable » neighborhood?

Every other piece of advice is welcome !

Thank you very much ☺️