the short answer is yes. a vpn will work and i do it often.
the harder answer is how it is all setup. and i am not an expert on networks so i am not the best to answer these questions. when we have had issues, our trimble distributor was great in helping.
i can mention that we have the network key installed on our office server computer. i am not sure if this is critical or not, or maybe you can just select any computer on the network because there is a dropdown to select which one it is on. as you seem to be doing currently.
the other thing that i have done in the past is force the computer that is searching the network to ping the server computer. this can happen in the searching computer s hasp licence settings.
also note that you can “take out” the network licence as another option. does not sound like this will solve your problem of trying to use the key with two computers on the same day. but it can be handy if you are going somewhere without an internet connection.
also note one more annoying thing. tbc does not seem to have an easy warning that someone is using one of the seats. it will just show no license. you likely can see if a seat is in use in the hasp software, but that is just one more thing to monitor. so some communication with your team is likely needed.
hope this helps a little.