That'd be a great thing to do, it'd take a hell of a lot of setup, but I believe it would be possible.
You'd first need a Video for Windows compatible external tv capture card to capture the signal from the first TV and send it to the first laptop. Specifically Video for Windows so you're less limited in the software that will work with it. That's the easy bit. The tricky part would be sending that signal to the second laptop. When it's there, you can set up the garden tv as a second monitor assuming the laptop in question has multi-monitor support, then all you'd need to do is display the full-screen streamed video on the second laptop, and the signal would be duplicated on the garden tv.
As far as sending that image from one monitor to the other, that's not straightforward. In theory you could use something like some Remote Administrator software, like
Radmin, which would duplicate the first monitor's screen onto the second, but I'm not sure how good the colour quality would be, and whether the video capturing would be accurately recreated. I can't think of another way to do it at the moment, perhaps an easier way will come to me.
Probably a better way to do it would be buying a dedicated Wireless sender, like
this one, thinking about it. Less messy, too.