When it comes to family portraits, I always imagine the the awkward posing in front of the camera, the need to wear what and pose would seem the most picture perfect in that moment to capture the most ‘perfect’ looking family.
The modern day famous family portraits tend to be of celebrity families such as the Kardashians, which have recently gotten a massive spread in Cosmo magazine. They are famous for, honestly, nothing very substantial except for being dysfunctional and rich.
I guess nothing much has changed from the past as most famous family portraits are commissioned by rich patrons as in the past, in order to commission such pieces, I believe, cost a lot of money considering the amount of skill required to capture such detail.
If I were to take a family portrait now, considering it is much cheaper to do so, I think it would be fun to try to emulate portraits of the past in modern day settings. At the same time, I think it would be rather interesting to have what you would call a modern day family portrait, but have it painted in a classical style. I think that would be pretty cool. 
I mean, can you imagine sitting like this for hours on end to be painted? I think that would be pretty funny but also very antagonising. 8)