I don't know the definition of tree miller...
[EDIT: as the video I linked to disappeared, thank Robotnik for pointing this out]
But there are a variety of semi-automated tree harvesters out there that are capable of a modest amount of AFK.
The idea is for you to have saplings in your hand, plant one, have a bone meal dispsenser adjacent, which bone meals the sapling.
Once the sapling grows into a tree, a large redstone device, which surrounds a 5x5 area pushes the logs out to a large wood collection area.
If you are daring, you can build an enclosure for a wither, and have the wither blow up the wood, most of which will get harvested.
Saplings are collected in hoppers at the bottom, and moved back to you, so you just have to sit and plant saplings.
There are many tutorials on the topics, in particular, google: Minecraft automatic tree farm (or minecraft AFK tree farm). A video from a more famous youtuber than previously posted is here:
This appears to be a known bug that Riot is working to fix (click the Riot logo next to "First Riot Post" in this link):
http://na.leagueoflegends.com/board/showthread.php?t=2721861
A few people have reported it fixed as of the last patch, so chime in on that forum post if you're still having trouble after patching! And make sure to submit your logs any game the sensitivity bug occurs.
Best Answer
This may not be to do with your sensitivity. I run Minecraft on a low-spec machine and also have this issue when I change priorities.
The issue here is that when you increase the priority of Java, you're making it higher priority than your mouse drivers. This means that when Minecraft is taking a large amount of processing power, the part of your computer which tracks your mouse is forced to wait- causing you to lose mouse control.
The obvious solution here is to not mess around with the priority settings and set Minecraft back to normal. If you have framerate issues, there are other solutions- I recommend Optifine. I recommend this, since screwing around with priorities can often have odd or unforeseen effects.
An alternative would be to find the process(es) related to your mouse drivers and ensure they are at equal or greater priority to Java's. This should stop the mouse issue.