Synergy is a great free application that runs across multiple platforms (Windows/iOS/Linux) to let you control multiple computers with only one mouse and keyboard. Sometimes it doesn’t work too well if one of your computers has to have a constant connection to a corporate VPN and the other computer does not.
Change your local IP scheme to something different than the VPN scheme. For example, if your local scheme is 192.168.1.x and you’re corporate VPN is 192.168.1.x, you won’t be able to connect. Change your local router IP configuration to be something different like 192.168.2.x. This worked for me.