Start with the pre-shoot consultation with both parents and outline how the shoot will be done. Convey to them that YOU are the one to get the smiles, the laughs, the expressions, and that they are NOT, under ANY circumstances, to "look at the kids to make sure they're smiling" ands they are NOT, under ANY circumstances, to even talk to the children. I'm serious...this is so,so,so,sooooo important. Parents can ruin a set by making a kid feel picked on, angry, upset, single out, etc. Many parents are pretty "wound up" about a family photo session, and the picture-face frozen fake smile and the every-shot-must count mentality from the film era still lingers on in many families. Parents will often be very nervous, and can easily snap at a kid for the slightest perceived lack of cooperation. I can not stress enough how critical it is for you to understand this, and to tell the parents beforehand that you must be allowed to run the entire photo shoot, and that they must not say a single word to the kids! No teasing...no coaxing...no coaching. no expression monitoring. Moms looking downward and across the group at a kid in front of Dad....ruins many shots. Parents literally ****ruin**** many sessions when they try to get the kids to do anything, the kids get upset, and then the session has to be brought back on-track.
Start with the mother, singles of her, shot as verticals. The Dad will take his cues from the mother. Shoot mom's singles first, then mom + dad as a couple, then Dad as a solo subject, and THEN bring in the wife and kids and start on the family as a whole. Trust me--woman first, couple, man alone, then family, then kids, then finish up with some breakouts of "the boys" and "the girls", and any blended family variants or special requests, like one kid + trophy or award, etc.,etc..
The basic idea is that with a fixed camera, you get people to LOOK at your face, and you can tell jokes, play-act, coach, direct, on an as-needed basis, first for an adult woman, then a man and his wife, then a grown man--who will be the most-insecure, reticent subject of the whole family 9 times out of 10. Mom will set the tone, and the others will follow her lead. With the kids watching how mom and dad act in segment 2, the kids see the needed behavior that both parents will model. Dad alone needs to be shot fast, and well, and is the ONLY person you might consider shooting dead-last.
You need the parents to keep their mouths totally SHUT once the family unit is in front of the camera, AND also once the kids are in front of the camera, send the parents out of the room, so they will not "try to help", and ruin the photos.
If you have shot a few hundred family sessions, you'll know why this is the best general outline of how to shoot a typical M + W- 3 children type family. It's not about the lighting nearly as much as it is human psychology and normal family dynamics. Family members standing off to the side of the camera, making comments to other members, is poison. Spectators and peanut gallery people can draw the eyes terribly, so keep them directly behind you, facing the wall, or in an adjoining or entirely different room. The more experience you have, the more you know how to handle the personalities, but again...the peanut gallery members, no matter their age, need to STFU and let you be in charge of the picture-making AND the expression-unifying, and the expression solicitation and achievement. If you want to, print this post out, and let the parents read this. let them know that telling little Caleb to, "Smile big or no ice cream for you!" or any other helpful coaching, cajoling,bargaining, etc. is the best way to ruin their family pictures. The photographer's job is to run the entire session, and they need to let you be in control, and they absolutely need to shut up and follow directions, and to keep their eyes on you, and let you do your part without them cocking up the whole shoot by being "parental".