.22 Cal CO2 for Mom

http://www.crosman.com/custom-shop/#

2400 KT from the custom shop. Add scope, CO2, pellets, and the squirrels won't stand a chance!

Hammerli 850, is my personal first pick. If money is a factor grab a Beeman QB79 bulk fill combo from Airgundepot for a $150. If you buy tonite, the QB gets a free air venturi target.($20 value). The Hammerli also gets a free Air Venturi spinning target ($49 value) 
Of course both guns can be had for 11% off and free shipping. That d​rop's the QB down to $135 and the Hammerli down to $222.

Check the Spec's and see what is better for you. The Hammerli has a 100 FPS advantage and a Walther Lother barrel. Covering to bulk fill would cost another $50. But the 88g bottle will get you around 200 shots so bulk fill isn't a must. You can also outfit the 850 with a LDC from TKO that will kill the report ​down so low, it will impress.

2400kt is lighter than the hammerli 850, though NOT a repeater.

if she wants quicker followup shots, get the 850. If she is a fair shot and doesn't mind taking a moment to load another pellet, the 2400kt will be lighter for her and out to 25 yards just as accurate for pesting.

You want to hook her up a scope cam.. That'd make an awesome youtube vid! 80yr old squirrel hunter! 

Look at the QB78 or QB79. You can find them for about $100. The 78 uses 2 12 gram CO2 cartridges. The 79 has options for single or dual 12 g carts, 88/90 carts, or 9oz refillable tanks.

+1 for the Hamerli 850. Pretty accurate gun. .35 30 yard groups. Can also get it modified at The 850 Store for increased power (about 60 extra fps) and increased accuracy. I have one and even after getting into pcp's, I still love to take it out and shoot it.