The 6D will give you the FOV of full frame. You will not notice much else different from your crops. The AF is decent, mostly a center point system, it will have better high ISO performance and focus better in low light (only on center point). But, other than that, honestly you will not see some incredible difference in image quality that is appreciable other than subjective stuff (lots of people have anecdotal evidence from experience thinking something is dramatically better, when its measurably not really). But the 6D will again give you the control over FOV and depth of field that really gives a full frame sensor its purpose for portrait (I use portrait here as that's your intended use).
The 5D3 will give you the experience that is both full frame (for FOV and depth of field purposes) and the AF engine of a 1D series Canon. This will give you the overall feel of what a full feature, no crippled options, full on pro-sumer body is all about. This one will give you the ability to use outer AF points accurately, not just center point. Plus all the other benefits of a larger sensor. So if you really want to take advantage of the 50L or 85L to test it out, this would be the superior camera to play around with, because the AF is superior and gives you a lot more options beyond center point.
You also do not have to get the 85L or 50L. You could easily just buy a 85 F1.8 and get the experience in general. Or add a 50 STM or something. They're so cheap, you end up owning them instead of renting them. And again you will get a very similar experience with a full frame camera to get your feet wet. You can commonly get the 85 F1.8 used for $250 and the 50 STM is $100 new. That's so inexpensive you might as well own them versus renting for a portion of the price. Just a thought.
Another thought is to try a 24-70 F2.8 flavor zoom, instead of a prime. If you really want something great for family, a great AF system full frame like the 5D3 and a very versatile 24-70 F2.8 will give you everything you need for literally everything with your family.
I'd rent the 5D3 & a 24-70 F2.8.