I learned the same thing, Thorn, that only those receiving Communion should approach the communion rail. However, I never saw any custom the father going first and the mother second. What I remember is this:
If the child is too young to attend Mass, he would be placed in a babysitting room where volunteers took care of the child while the parents attended Mass or the parents would split up attending Mass so that one could be with the younger children.
Those too young to receive communion sat in the pews (and to the chagrin of the parents, sometimes misbehaved).
The reason, it seems to me, that this is not generally the case anymore is the fact that most traditional parishes don't have several Masses a day and/or families have to travel quite a distance to get to Mass even when there is more than one Mass scheduled. It is extremely inconvenient for families, oftentimes boardering on the impossible, to split up and since the congregations are mostly smaller they have a much smaller pool from which to solicit volunteers for babysitting (if they have more than one Mass).
Even in those few chapels in which this is no longer the case, nearly all of them started out in this situation.
Thus, over the years, many parents began taking very small children with them to the communion rail. (I've never seen a traditional priest give these children blessings as they do in the Novus Ordo churches where even the "Eucharistic Ministers" blesses little kids with their hosts.)
I think this current "custom", so to speak, really grew out of necessity at one time and it is oftentimes difficult to change midstream, especially in an area that really doesn't have to be a problem.
At my chapel, there is a family of eight children. The youngest of them do often go to the communion rail with the parents while the older ones who have not yet received first Communion usually stay in the pew. Sometimes, though, as children are often wont to do, these older children just will not stay in the pew and come up with the parents as they used to do. They do not create a disburbance and there is simply no disrespect shown to the Blessed Sacrament. The altar boys know who can receive Communion and place the patten under the chins of those who will receive and the priest gives Holy Communion. Then they simply go down the line to the next person who will receive. Again, there really isn't a problem.