I have two different ISPs from two different providers, each attached to its own router, coming into my PC over ethernet. One is a personal account and the other is for work. My problem is that the Dynu Update Client defaults to my home computer when I really need it to manage the other one. I can get it to show my "work" IP address by disabling the "home" router, but is there any way I can set it up to default to my "work" connection permanently?

My company have 4 internet connections. I have tried your method.

Easiest way to is the update the IP from a device that has the right connection.

The more difficult trick I used is to modify the routes on your PC. Based on the target IP, you can choose the gateway/interface.

for example, you may specify 0.0.0.0/0 on your work internet gateway. remove 0.0.0.0 on your home internet.

Or maybe you can set 162.216.242.0/24 (api.dynu.com) low metric on your work connection gateway, then 0.0.0.0/0 high metric on your home internet gateway.