That's even impossible in your home network (a LAN), let alone across the Internet. See this recent discussion also: https://www.cnet.com/forums/discussions/how-to-setup-a-software-server/
I know you can run software from the cloud without installing it, for example on a Chromebook. But then you would need your own cloud server to install it on, and that's quite something different from the main computer at the shop. All you can do: install all programs locally and use data in the cloud. Some programs (such as Office 365 from Microsoft) are designed for that.
I am not exactly sure what to call it but I am looking for a way to have a main computer set up with all of our software, programs, and files and be able to access them from anywhere over the internet. I know this is easy with the files but I am not sure how to be able to use software on my personal work computer at home when the software is installed on the main computer at the shop. Is this even possible and if so what do I need to do to do this?