Family Boarding allows one child, age six and younger, to board with one adult. Family Boarding occurs between the "A" and "B" boarding groups. So, unless you are looking to sit within the first several rows of the cabin, Family Boarding should provide good seats for all of you, sitting together, at no additional cost. If all in group have "A" boarding numbers, then you can board together.
Normally, Early Bird would not allow anyone, other than the ticketed passenger with EB, to board in that particular boarding position.
Your other option would be to purchase Early Bird for one adult + one child, with the other adult and child boarding in Family Boarding.
Keep in mind that purchasing Early Bird does not guaranty an "A" number; sometimes EB assigns "B" boarding positions, depending on when EB was purchased and how many others purchased Early Bird, before you. That could mean that Family Boarding would allow you to board earlier in the process, than EB position.