Joseph Smith once said something to the effect of if one could peer into heaven for 5 minutes they would know more than after reading everything ever written on the subject. And I couldn't agree more.
Basically the LDS belief is that if you are "sealed" to your family and live worthily, etc, gaining more knowledge and becoming more like God as you are commanded to by Christ ("be ye therefore perfect even as I and your father in heaven is perfect") then you can live with your family in the highest degree of the celestial kingdom where God is (according to a vision and a revelation had by Joseph Smith).
A lot of member will accept polygany as one man can be sealed to his wife and if his wife dies he can be sealed to a second. However, a lot still take great offense to this. As far as Polygyny is concerned the answer is that yes, we believe it fits in with heaven and if you don't like it you'll have to lump it.
Personally I can say that I don't have a clear idea of what heaven will be like, it's something I have recently found myself trying to search out in the scriptures and revelations. But I feel confident that it is a much nicer place than even we could now picture and we should strive to live like someone who belongs there. As I don't believe we are all magically going to be made perfect, unfeeling beings.