Okay, good. I wondered if you’d actually measured it. 
That measurement doesn’t totally surprise me, because with the 16V 10VA transformer I’ve used with my Video Doorbell v2 I’ve consistently read in excess of 18V when measuring with a digital multimeter. If you’ve been able to measure your mom’s transformer’s voltage, then you should also have the ability to confirm and test the wiring within the system so that any new chime (and/or transformer) gets wired correctly, and the installation should be pretty straightforward from there.
The thing that does surprise me some is how far out of the rated specification your measurement is: If it’s rated for 10V but you’re measuring 16V, then that’s 60% over spec, which seems like a lot to me. Because of that, the transformer’s age, and the low apparent power (VA) rating, I’d be inclined to replace it with something newer that’s rated for Wyze’s stated requirements.
The thing I don’t know about Wyze doorbells’ transformer requirements (all of the current models specify ≥10VA & 16-24V AC[1]) is how necessary the apparent power output is. Your mom’s current transformer is rated for half of Wyze’s requirement, so I’d be on the lookout for problems related to inadequate power if you proceed, things like the camera losing its Wi-Fi connectivity, flaky chime performance, or other aberrant behavior. My recollection of other Forum users’ experience with this is that replacing the transformer with something that meets the recommended ratings can solve those problems[2][3].
One other thing I wondered after my original post relates to the current chime. If it’s dependent on someone holding in the doorbell button in order to make it ring for the duration of the press, then I’m curious if it would be possible to connect an adequate transformer and Chime Controller into the system with this existing bell and use Video Doorbell v2’s Digital Doorbell Chime Type setting with an appropriate delay/duration (“Ring Tone Length”) so that a single press of Video Doorbell v2’s button would allow power to pass through Chime Controller long enough to get a good ring from the current bell. I don’t know if something like that would work or not, and I don’t know enough about the wiring in your system to suggest anything, but it’s something I’d probably play with myself in that situation (because I’m curious and stubborn).
The easiest and most straightforward solution here is likely to be replacing both the transformer and mechanical chime, though. It will be an adjustment for your mom to get accustomed to hearing a traditional ding-dong doorbell, but that’s what I would expect to cause the least amount of headaches from an installation and troubleshooting perspective.
The product page for Duo Cam Doorbell actually says “10-24V AC”, but I don’t know if that’s accurate, because articles within the Help Center for Duo Cam Doorbell specify that the “existing circuit must have a minimum voltage of 16V”. ↩︎
Wyze Doorbell Cam v2 disconnects and stops working after a few days without a factory reset - #4 by john-meek & Wyze Doorbell Cam v2 disconnects and stops working after a few days without a factory reset - #5 by john-meek ↩︎