The conclusion I've come to is that the hardest negotiations are the ones that hit closest to home, where people's emotions get wrapped up in the negotiations and they no longer think rationally. In these cases, people become overwhelmed by their emotions, and even if they have the knowledge and skills they need, they lose the ability to negotiate effectively.
The most important skill in such situations is to recognize what is happening to you as it happens, to become more self-aware in real-time. If you can not recognize your emotional responses, you have no chance of modifying your behavior. You then need to develop tools to slow the negotiation down so you can manage your emotions as you negotiate, with the goal of staying deliberate and strategic rather than reactive.
This is not an easy thing to pull off, especially since you will be under emotional stress at the time, but given time and practice, you can learn to manage your emotions and negotiate more effectively even when the negotiations are highly personal and trigger strong emotions for you.