Core business application that will only run when logged into PC as an administrator

I am about to take on a new customer. They have some issues that I want to address before agreeing on a monthly support arrangement.

The main issue that they have is that they have an application that will not run properly unless the user has admin rights.

The PCs are running either Windows 7 or 8.1.

According to the staff there, the application will not run if you try to "run as administrator" . The user themselves have to be local admins on the PCs. The network is a peer to peer set up with no server.

This obviously causes issues. We are pressurizing the software vendor to resolve the issue and my customer is unable to use an alternative.

I have to find some way of securing these PCs whilst still allowing access to the troublesome system.

I thought that maybe hosting the application on a RDS server might be one solution. Perhaps an Azure VM.  Just publishing the Application.

Does anyone have any thoughts on this option or do you have other ideas?

Thanks