Nodes are expensive (about $500 each for the cheap ones). So you don't want a bunch of miners sitting around idle, just waiting for a fork to jump into action and try to resolve it in your favor.
If you have the Nodes, you'd rather have them working than sitting on the sideline.
Nodes don't get to automatically, instantly "Vote".
The miners decide which block is going to be "accepted" by mining the next block, using either of the two branches as their previous block.
To further a chain a node has to solve the next block in the chain. This is a very hard problem to solve: with all the Mining Power in the world, each block takes about 10 minutes.
It is not clear what "advantage" one would get from favoring one accepted block over another. Naturally, you prefer your own block (so you get the reward and fees), and the other Miner prefers his block (for the same reason).
But every other node in the world can pick either side, they don't really care which side wins.
Once the next block is mined off of either branch, the problem is pretty well decided. If both branches are again solved in roughly the same time, you still have the fork to be resolved on the next block. But forking generally gets resolved within the next 2 or 3 blocks.
Orphaned blocks happen pretty regularly (https://blockchain.info/orphaned-blocks)
When people refer to 51% of the miners, they mean in the long-term, once one branch of a fork has more miners (processing power) on that branch, the "losing" side has to do more work in less time with fewer resources than the winning side, just to catch their branch up to the "winning" branch. That is a virtually impossible task; so the losers just rejoin the main branch.