Generate random numbers given a set of constraints

I had an application that required something similar to the problem described here.

I too need to generate a set of random variables {Xi} that add up to a given sum S, where each variable might have constraints such as mi<=Xi<=Mi.

This I know how to do, the problem is that in my case I also might have constraints between the random variables themselves, say Xi<=Fi(Xj) for some given Fi (also lets say Fi's inverse is known), Now, obviously the random variables can't be independent since setting Xj gives knowledge as to the possible values of Xi but how should one generate the random variables "correctly"? I put correctly in quotes here because I'm not really sure what it would mean here except that I want the generated numbers to cover all possible cases with as uniform a probability as possible for each possible case.

Say we even look at a very simple case: 4 random variables X1,X2,X3,X4 that need to add up to 100 and comply with the constraint X1 <= 2*X2, what would be the "correct" way to generate them?

P.S. I know that this seems like it would be a better fit for math overflow but I found no solutions there either.