The First Class (Upper Class) lounge for Virgin Atlantic in LHR has a game room (various arcade video games) and a music room (the only 'drawback' is only Virgin Records artists).
The First Class lounge for LH in FRA has no 'family room' but our then 16-mo son enjoyed it. There were another family in the lounge with two young boys. There were a total of seven people in the lounge and there were eight LH employees in the lounge.
The US Airways lounges at the PHX airport is NOT kid-friendly. One time when my son was 2, an US Airway lounge employee tried to kick my son out of the lounge when I went to the restroom. My wife and son were sitting by the very edge of the lounge (closest to the desk and entrance of the lounge)...at least 30' from another guest...when my son started to sing "Old MacDonald' in a very low voice (not screaming, not the typical loud kid voice, etc...I asked the another guests and none of them heard him at all). I did not renew my US Airways lounge membership when it came up for renewal.
The Maple Leaf lounge (Air Canada) in YVR doesn't have any kids\family rooms but it is very large enough that children don't get in the way of other passengers. We have been in that lounge a few times with my son without any problems.
The Alaska Boardroom (Alaska Airlines' lounge) in SEA is very nice and has two floors. I have seen children in there but most went to the 2nd Floor. I have been in that lounge over 20 times but never went to second floor since I like the desk, work spaces, cisco phone systems and etc. on the first floor.
However, SEA airport has a children playground with a family restroom.
I am not aware of any lounges in the PDX airport that has a chidlren\family room. However, there is a children play area and TV in concourse C.
I am not aware of any lounges in the CLT, TPA, SLC, LAX, LAS, ORD and ATL that have chidlren\family rooms. The 'new' CO Presidential lounge in IAH might have a children\family room...it is outstanding and is very large (I think two or three floors).
When we go into a lounge with our son, we just tell him that he needs to be quiet since other people are there working. He has been very good 99% of the time. We do tried to sit in a 'remote' area. Occasionally, he will laugh loud but it is no louder than the adults in the lounge talking loud on their cell phones telling everyone how important they are or how ignorant they are, the obnoxious drunks, etc.