This is the joint distribution of two order statistics from a sample of two.

You can find that in many books.

I think it's in Wackerly, I used to use Hogg and Craig.

since you only have two observations...

There are 2! ways this can happen.

Either Y1=X1 or Y1=X2.

The reason it's still a valid density is that we now have a restriction on the space.

The order statistics are dependent.