Both are possible, but mean different things. Consider these simpler examples:
This phenomenon has been observed in the atmosphere, where condensation almost always forms around dust particles.
In the atmosphere, a phenomenon has been observed where condensation almost always forms around dust particles.
The first sentence refers to a phenomenon from the wider context, usually something that was previously described. The second sentence only makes a statement concerning what happens "in the atmosphere".
Likewise for your two sentences:
This has been proven obvious at the Colorado Center for Reproductive Medicine, where it is not uncommon for expectant grandparents to come along and offer support and quite...
At the Colorado Center for Reproductive Medicine it has been proven obvious that its not uncommon for expectant grandparents to come along and offer support and quite...
The first refers to something that was mentioned before and can be observed to hold true "at the Colorado Center", while the second only states something about "the Colorado Center".