OK, there is something strange here. And, Carl's idea seems good. But, this shouldn't be your issue. It should be AC's.
So, there is an issue with Citrix. Citrix has support. You don't have access to that level, but AC does. In other words, AC support pay them to use their product. So, if it isn't connecting, I would think it is up to them to get support involved and log in.
Another way, which would be simple, would be to make sure you can RDP from one computer to the computer you need them to access. They could then remote to the other computer and access your problem computer remotely over your network.
When you have a question like this, it would be helpful to us if you give us more information.
What is the OS? Home or Pro?
What version AC is it? Just helpful to know.
Even if they can't get from good computer to problem computer, can they log into one of the good computers?
And, what is the issue? It may be we could suggest something to fix it.
But, I would call support and set up a time to remote in. You are paying for support. They should spend as much time as possible to make it work. You shouldn't just let them say, well there is something wrong with your computer.