Regarding the possibility of leaving them alone - it depends in a large way on how you've written the children, and their ages. I was fine to be left alone for short periods of time (like, half an hour or so) from around age 8. I was asked to look after my younger brother for similar periods of time from around age 11. (He would have been 7.)
I was a hyperactive but reasonably responsible kid.
There's also cultural norms to consider. What I described above was pretty normal for middle-class Australia in the 90's. It would probably be regarded as child abuse in America in the 2020's. And in Japan, 6-year-olds are sent out alone to buy groceries. They really like their kids to be self-reliant from a young age.
Also, what's their mother like, personality-wise? Does she value independence and self-reliance? If so, she's probably raised her children to be reasonably capable of doing a lot of things on their own. They'd probably be fine home alone for a few hours.
On the other hand, if she's a worrywart and tends to helicopter around her kids, they're very unlikely to be okay on their own, nor is she likely to consider leaving them. My sister-in-law is like this, and her eldest boy can't really do anything by himself. He's never been allowed to. In this case, your character would probably take them with her, or refuse the call-to-action if she couldn't find somebody to watch them.
Let your characters and their natures lead you, and I'm sure you'll make a choice that works for them and for your story!