Yes, you need more RAM. Vista cannot run being choked down like this. It's like an 80-year-old chain-smoker trying to run the Boston Marathon (worse than that, actually, but you get the point).
My Mom's old Acer had Vista Home Basic on it...512MB RAM, 1.86 GHz processor, etc....you could just about go cook a meal by the time the darn thing booted.
Yes, adding RAM will increase performance slightly, but Vista is still Vista. You won't see the performance you can get out of XP or even Windows 7. You can "optimize" and "tweak" all you want, the effects will be negligible. Putting 2GB of RAM into it will increase the speed up to a point (you will notice a considerable difference), but that's as far as it's going to go.
Personally, I don't think it's worth it to waste time and money on a computer like that. If it were me and I had the money, I would just trash it and buy a new laptop with Windows 7 on it. If she's tight on cash, you can get last year's "high end" models for around $500 (depending on who you buy from), which much better specs than what she's currently running.