knowing what type of router you have would be of great benefit.

Probably the only thing which will change her mind is a sound business case & consultation with experts. Unless it's threatening your job security, and it might be the way things are going, it may not be your problem.
The hotel must have some familiarity with your ISP so you might be able to get them to help as the experts.

I've helped many clients set up and maintain a VPN through various devices but i unfortunately don't have much experience in the adminstration/security departments for them. I wouldn't have thought that a VPN would be a threat to your network any more than allowing clients to connect to it for internet access, other than the configuration of a few ports on the router.
Presumably you have all the common file sharing ports turned off and only allow traffic between the rooms and the internet not between rooms.

I'm sure if you were able to get more information we could help you develop this idea, if you wanted.