The first time we traveled with our oldest daughter almost 6 years ago when she was less than a year old, I inquired about family preboard, and the GA laughed at me and said that United stopped doing that a LONG time ago.
We travel a lot as a family on both United and Southwest. The reason you need early boarding for families on Southwest is because there is no assigned seating. You want to make sure parents and kids are able to sit together. This is generally not an issue with assigned seating.