On youtube, I would just contest the copyright holders.
For it to be fair use you need to be able to ask these 4 questions (not all 4 need to be good to be fair use):
1. What are you doing with the copyrighted content? If you are doing something highly transformative with the content then you will have more room under the fair use doctrine. You are more likely to be covered if you are saying something quite different from what the original creator was trying to say.
2. What is the nature of the copyrighted content you are using? Use of creative or fictional content (for example, a film or cartoon) is less frequently allowed under fair use than less creative, non-fictional material.
3. How much of the original content are you using? You should be careful to use a reasonable amount. Just use enough of the copyrighted content as you need to in order to get your point across.
4. Will your work serve as a substitute for the original? If your video will take away views or sales from the original then it is less likely to be covered under fair use. Additionally, you shouldn’t create work that occupies markets that copyright owners are entitled to exploit.
The thing you need to realize is EVEN if you are fair use, the copyright holders can still sue you and the courts will then need to decide if your usage of the material constitute fair use. Home movies are protected by fair use. Feel free to contest them, but again depending on length and use, see court case of a 29 second home video, Lenz vs Universal
Now the other issue is that contentID system was abused by the rights holders and there recently has been pushback by youtube.
"YouTube also is noting that it had updated its ContentID tools to try to avoid some of the excessive takedowns associated with it. For one thing, it appears that "certain rightsholders" are being asked "to perform in-depth audits of their references before they can make any new claims." Reading between the lines, that sounds like YouTube is hitting back at rightsholders who have abused ContentID. That sounds good, though we'll have to see how it plays out in practice. YouTube is also making it easier to pull out incidental audio in videos that might trigger a ContentID claim, improving the way MCNs can "fast track" a response to claims they think are bogus, and is promising to more aggressively investigate ContentID abuse."