Just my few pence worth. As Bobby says, damping is really important and a few clicks on the front or back can solve or create problems.
Unless you have posh dampers then your bump (squat) is basically fixed and your rebound (lift) is adjustable. So to stop the weight moving forward you need to increase your rebound (number of clicks) at the rear.
So you increase your rear stiffness to the max to get no weight transfer and stop the skittishness right.... err wrong. As soon as you turn the wheel all the weight now goes to the outside front and the back end skids.
So what's the right answer...... there isn't one, you have to try it yourself.
You can use my zen budhist handling guide that no bu**ger understood so I stopped writing it but comes down to if you need more control go stiffer, if you need more grip go softer. As you say you are losing rear end grip under braking either stiffen the front or soften the rear. In general try softer first but sometimes you might soften and you lose control of the spring in a different situation so the only option is to stiffen the other end.
So bobby might be right but for all the wrong reasons
Incidentally, the rear of a car squats with the hand brake because of anti-squat designed into the suspension for acceleration that works in reverse under braking. Subtle stuff that whiteline barely understand if you read the theory justification that is pro/anti-dive/lift kit.
So read that last comment again and start to understand why increasing the rear brake amount can improve stability at the rear end. Increase your braking past the point of available grip and you skid again....simple.... not