That might technically work, althogh I'm not sure if health data will sync back to the iPhone via Wi-Fi or if it needs to have a direct Bluetooth connection — it definitely required a direct connection originally for privacy and security reasons, but now that Apple allows health data to sync with end-to-end encryption via iCloud it may have extended that to the watch, although I wouldn't count on it as Apple doesn't relaly have any incentive to add direct sync, since most Apple Watch users have their iPhone nearby more often than not.
Even if this would work, however, I'm not sure you'd want your mom's data mixed up in your own Health app, since even though you don't own an Apple Watch, there's other data that may still get recorded in there. You'd have to make sure you don't use anything at all that ties into the Health app (e.g. exercise or diet apps), and even turn off things like step tracking, emergency SOS, your own medical ID, and of course you'd have to enter all of her stats like date of birth, height, weight, and so forth. The Health app is designed to track an overall health profile, so it would be weird having heart rate and blood oxygen data from your mom combined with your own step count, and some of the recommendations the health app would come up with might get skewed if there was a mismatch — conditions that might warrant an alert for an 80 year old woman wouldn't necessarily move the needle for a healthier 45-year-old.
Personally, I think it would probably be best just to pick up an inexpensive iPhone to pair with her Apple Watch. Even the 2015 iPhone 6s and 2016 iPhone SE support iOS 14 and can therefore still be used with the newest Apple Watch models.