Let's make this simple.
-If you don't scan the BP, JetBlue will bill you and/or terminate the Mosaic account.
-If you try to checkin with the 3 of you, the agent will get suspicious and raise a reg flag.
-If you do online checking and have just one person checkin bags, and tell TSA the baby's name is the Mosaic members name, and hand over the 3 boarding passes to be scanned at the gate, the odds are that it will go OK. But if you are busted you could be in trouble with both JetBlue and the law.
-If you want to be safe, stop trying to scam JetBlue and cancel the mosaic's ticket now.
May the odds be ever in your favor.