Secure Internet-Connected Jumpbox/Console

So I've been doing my own research as well and have several ideas for how I could do this but I'm looking for the most seamless and secure option, figured I'd post here and farm the idea out. Essentially what I'm looking for is a kind of remote console that would be secure, internet connected, and give me mouse, keyboard, and video on a second machine.

I realize I could very easily just connect directly to the second machine but the expected failure is going to be VPN related so my ability to connect to it would be tenuous. My thinking is a second box that has direct control over the first and can always be accessed to perform remote control when the first box cannot.