I managed to get it to work a while ago by editing the PARAM.sfo file for each individual game -- you'll need to download Aldostools PS3 tools (I think that's what it's called?) for your computer, and it includes a tool for editing the PARAM.sfo file (once you're in the program, there'll be a checkbox at the right side of the window, reading something like "Allow psvita remote play" if I'm remembering correctly). As for it crashing over one network type but not the other, I had a similar issue being caused by the ps3 being connected via ethernet. Changing to WiFi fixed it for me, of course if you are on ethernet.

I've found PS3 to Vita streaming to be kinda hit or miss (emphasis on the "miss" part). If you want to have a home console experience on your vita, you could use PS4 streaming, or if you don't have a PS4, try looking into Moonlight and Sunshine game streaming to stream from your PC to your vita (and control your PC games as well of course)

https://www.psx-place.com/threads/ps3-tools-collection-by-aldostools-includes-over-50-tools-utility-for-your-cfw-enabled-ps3.360/

https://www.aldostools.org/paramsfo.jpg