Ever ask your Insurance Agent about storing your guns? You might get a suprise. Depending on the standard Home Owners policy where you live you could have complications for off premisis coverage and in the case of your mother would be a relative, without doubt, but not a member of her household. Suggest you check.
Regarding a safe, before you buy, measure the house, make very sure the safe fits the doors and angles it must pass through to get it into place inside the house itself. If I had a dollar for every safe purchased, that would not fit in the house after purchase, I would have a big pile of money. Fire and water proof, if you have a fire and a basement, it will go into the basement where it will sit in fire for hours or under water for weeks. You get access only after the fire marshal completes their investigation. Every person forgets this, water flows down hill and a fire dumps everything into the basement..
You as an individual will never stop a pro, you can stop the amateurs. Best defense is that Pros are not interested in any serial numbered items. So you protect against common thieves and fire. Worst thing in any house is your own kids and talking to their friends.