Loaded questions, since we know nothing about the modem and router at the vacation home. As it stands, we can only answer to the effect of you will not know if it will work until you try.
We also do not know how the Time Capsule connects now at your home.....to a modem....or a modem/router device.
Even if the router at the vaction home will allow a new device to connect using Ethernet at one of the LAN <-> ports, you should understand that anyone on the unsecured Wi-Fi will be able to "see" the devices on the Time Caspule network since everything will be on the same subnet.
If you want to use your Time Capsule to create a secure wireless network at the vacation home, it must connect to a separate modem.....not a modem/router combination device.
In that regard, do you know if the vacation home has a separate modem and router, or a modem/router or gateway combination device?
Most service providers furnish modem/router combination or gateway devices these days, and have done so for some time, so a good guess would be that this is likely the kind of device that would at the vacation home.
As a fall back, it might be easier to plan to use the unsecured WiFi and limit the connections to financial sites, etc during your stay. In other words, assume that you will be at a hotel using wireless, so what you would do there, you could do at the vacation home.
Hopefully, the home is secluded and isolated if you need to conduct banking, credit card etc. transactions.