As a photographer, i tell the parents to give the kids what they need in advance. Make sure they are warm, fed, had enough sleep. They may need some crazy spinning and dancing with mom and dad. I encourage mom and dad to keep focusing on their little one and be ready to provide all the snuggles they need.
* Invite, turn it into a game
Kids love to play. When you make something fun, they are more likely to get on board. Don't make them pose, make them play.
* Encourage interaction
Ask big brother or sister to count the baby's finger's or give a hug. Other times, I will have dad toss the child into the air or spin the child around. tickling contests, blowing bubbles-anything that requires movement or concentration will aid in capturing their true character.