I think "how to ask" might be to appeal to reason.
In most places if people or animals are killed there are laws concerning that but when it comes to insects it's more about the laws concerning pesticide and disposal, not about the insects at all.
If there's an insect in my home I have a 'catching jar' so I can catch and release them outside, if it's a flying insect I can usually open the window further and direct them outside - not sure if my neighbors have figured out or thought much of my example but it's there for them to learn from, if they are so inclined.
You might inquire of your mother's reasoning and what example she hopes to set ...
Is it that she's lazy with leaving food out and cleaning up, that the ants are simply little pests that remind her of this?
Is it more simply that she's big and they are small?
Is it because they are insects, what if it were a cat, dog, or bird; would she swat it?
Does she enjoy the extra mess and work of cleaning up the deceased bugs?
By asking what she is trying to do and how successful she thinks her efforts are might encourage her to be tidy and not take it out on the bugs.
What if she bugged the neighbors, should they be rid of her?
Maybe she fears being bitten or of disease, she is looking out for you. By asking what she is doing and why will better equip you with how to put forth your beliefs and solutions.
Telling people they can't go anywhere and walk outside because they will step on a bug is a non-starter; educating people about cleanliness and respect for others is likely to be an argument, a belief, that is better received.
Ask to get a frog or lizard to eat the bugs, that too will probably be rejected. Not leaving the burglars an invitation is the way to go.
Education and reason will work better than a conflict of belief.