we can look at this from another evolutionary psychology perpecstive. this is probably one fo those mathematical problems about maximizing the replication of your genes.
there is two purpose of life, gene survival/self perservation and gene replication. With the first, the second cannot occur. so in essence, money comes first..but there is a steep diminshing return on the utility of money...
money represent the means to self perservation and family represents the replication of your genes.
I think there are two scenerios:
1) you don't have a family(no children, few close relative) and surviving on bare subsistence,then of course, the answer is yes, because the money increase your chances of mating and the survival of your future offsping..
2) If you have a family and kids are young, unlikely to start a new family in the near future, then you have vested interest in your family .The answer is no, you are unlikely to give up your family for money.
this is of course a simplistic analysis, the real world is much more complicated, but I think everyone falls in between these two more extreme scenerios. generally, in this wealthy time, it doesn't make sense to trade money for family because you are not in self-preservation mode..
but it's noted that during famine in ancient china, families have exchange their own childern as food(barter as oppose to money)to cannbalise. which I guess makes sense from this perspective, if the family is not going to survive anyway, it's better to trade them for "money".
friends is a special case, they are form of "money", human capital, because they come into help when you are in trouble, but they don't share your genes and if you have real money, their value diminish in anyway. it's seldom that people give up their money for friends, and I have never seen people give up their family for friends.
given some assumptions and numbers, we might be even calculate precisely how much money would you be willing to give up ONE family member or one friend.. ^^