Pros:
Having another car can lower the miles you put on the Prius, retaining its value.
Having two cars (or vehicles) makes things a lot more tolerable when either needs maintenance or repairs - it also has potential to save money because either being out of service doesn't need to be resolved ASAP at all cost. If doing your own maintenance, you can go get parts or tools you need. If one needs tires (for example), you can park it until they go on sale.
If something should happen to you or the car, your wife can now come to your aid (or you to her aid).
Wife could get a job. Or a hobby, that contributes to 'happy wife'.
Cons:
Registration (cost varies greatly)
Points & Qs:
Can wife drive you to work (and pick you up)?
Can (could) wife ride a bike to shop?
Only you kayak? Why is a van or station wagon ok but not the Prius?
Where will you store a kayak?
How far will you drive to kayak? How often?
I have strong reservations against a $2000 vehicle. Safety and reliability have value, and costs. You usually get what you pay for... I admit this is my personal opinion.
If you (the plural 'you') find that your wife doesn't drive that often, you could rent out your second car via turo.com (not sure if they are active everywhere). The car has to be new enough and nice enough. Your wife could decide when she needs or wants the car and rent it out other days. You 'could' rent out the Prius, but (personally, again) I would never rent out my personal car.
Speaking of options; is Uber available in your area for her to use to shop when needed?