I have something like this with tail scale. My homeserver has a tail scale docker as well as a docker tail scale. The docker tailscale advertises itself as an exit node. The tailscale docker is gluetunned to an extern wireguard server (your mullvad for example) Now I can connect to my home net with tailscale and toggle the exit node on and off. By adding a different tailscale container with a different wire guard exit you could just toggle the exit node like that.

Seeing as you are using mullvad you could also just pay the monthly sub to tailscale and they connect your tailnet directly to mullvad