That sounds like a royal pain in the ass, we had a couple communal PCs at work and every time one guy would use one he would sign off locking it. He would swear he didn't lock it but only his password would unlock it.
The computers you're running remotely, are other people at those locations getting information from them or are they running other machinery or something?
 

a meeting with the vendor on my desktop and give them mouse control of the remote session

i am the vendor

sir the best way to approach this is to click this box see this box right here where my mouse is moving? yes and preview the output when it returns, that way you can see what the executive appliance is actually changing. yes and i like to save the output, you do that over here, see where my mouse is moving? and copy it to the master server and even do a diff to compare it to the current configuration. that way you know exactly what happened. you can even back up that configuration if you have multiple changes. see this tab over here where my mouse is moving? set it up there and it saves it automatically, so you have a record of what happened each time for audits. we have a knowledge base article on the support site that explains all of, well most of this, ha ha. KB048. yup. yup. no problem. i will close the ticket and you have a great day. bye bye.
 

it's better than them having control and trying to explain what they have to do

"then go to the middle tab. not the excel tab, the exec screen. the middle tab. ok you need your sign in. Or Pam's. Pam's would work. OK now go to Tools. no on the exec screen. Tools and then Collect Utilization Report. it's at the bottom. no the bottom of the Tools menu. yep right there. click it. actually you don't need to double click it."