If your mom doesn't like conditioner, she might be intrigued by the idea of a pre-shampoo conditioning with either conditioner or with a small bit of oil (couple drops) really worked into hair and scalp. Coconut is great for grays, but otherwise it can be too heavy for fine hair and almond or apricot kernel oils might be better.
Spray-on conditioners are great for fine hair.
When my hair was very short, I never used conditioner and my hair was super-healthy. I did make sure to finger comb/massage my scalp it before washing to distribute the sebum - although if your mother is over 50, her skin is probably less "oily" so a bit of extra oil is a good thing.

I liked Burt's Bees Super Shiny conditioner as a rinse-out and leave-in in the past (allergic to an ingredient now). It wasn't too heavy. Conditioner leave-ins do help with frizz, but with fine and very short hair, we're talking a very small amount.

Teasing really ruins hair. Look at this photo: Hairdresser Austin, Texas - Hair Color Specialist - Board Certified Master Haircolorist Specialist- Sandy Kurtzman, Master Hair Colorist - Austin Hair Salon - Austin Salon - Color Salon Clipping works great, but it takes some learning and dexterity (and styling product). And some "root shaking" to restore fullness when dry.

My mother has thinning hair which has always been fine and "curly" (big, loose curls - probably wavy curls, it's been short all my life) and she keeps it really short (see-your-scalp-short) and I made her a lovely protein-enriched conditioner which makes her hair shine. I would love to show her how to clip for volume and so on, but somewhere in there I'd be crossing the "bossy" line and imposing my values, which would turn her off! Moms are tricky. I'll wait for her to ask me, or to be able to drop it into a conversation like, "Remember how flat my hair was as a kid? It still is, but I learned a trick..."