It is my understanding that you can use an RCA interface with a Raspberry Pi by using a 4-pole 3.5mm jack (image below) - I have a portable screen with RCA inputs I'd like to solder directly onto my Raspberry Pi. Once I snip off the female RCA connectors off my portable screen, what solder points should I attach the bare cable to?
No, please don't do that. Unless you have a dozen Rpi3's to play with.
Here is a better idea:
http://www.instructables.com/id/Raspberry-Pi-2-Quick-n-Easy-RCA/
I am dubious to the need for composite output when HDMI is available and nearly universally available as an input. Plus, there are external HDMI-to-composite converters that do not require any Rpi hardware alterations.
Even with the above, (Quick-n-Easy-RCA). there are software issues. Without resorting to extensive cut-and-paste, here is the best link today:
Cheers
Use continuity/<=200ohm test on your DMM to ensure you solder the wires correctly. I used a small metal file on my female jack so the solder would bind better.
It helps to use 400° and be real quick about it. I’ve often done this on TRRS audio jacks, and if you delay too long the plastic insulating the different connections will melt. This happened on my first try. Best to test it on some of these TRRS jacks before you do it on your Pi.
GND will sink more heat before you can solder it, so use leaded solder for that connection. In fact, it’s best to use leaded fluxcore for all these connections, not the unleaded hippie stuff.
Use as big a tip as is practical, and to ensure you haven’t made a cold-soldered joint, give it a wee pull when you’re done.
I use a tip like this (for a TS100): 
