I wouldn't do it myself, according to the manufacturer they are supposed to be on a firm surface and it specifically isn't supposed to be used on a bed. Especially with a preschooler and 2 adults shifting the surface of the bed, I just wouldn't be comfortable with a baby sleeping on something like that that is so stuffed. They specifically warn against using it for sleeping. Here is the warning I saw for the product on Amazon:
WARNING: TO PREVENT SERIOUS INJURY OR DEATH: DO NOT ALLOW BABY TO LIE FACE DOWN OR ON SIDE IN THIS NEWBORN LOUNGER. ALWAYS USE ON THE FLOOR. NEVER PLACE IN THE CRIB, ON THE BED, TABLE, COUNTER, OR ANY ELEVATED SURFACE. NEVER MOVE NEWBORN LOUNGER WHILE BABY IS ON IT. NEVER LEAVE CHILD UNATTENDED. WARNING: this product is appropriate for infants up to a maximum of 16 pounds, or until the child can push up on hands and knees or rollover on his own accord(whichever comes first). To prevent serious injury or death: Do not allow baby to sleep in this pillow. Always use on the floor. Never place in the crib, on the bed, table, counter, or any elevated surface. Never leave child unattended. Keep away from heat source or open flame.
It is super cute and I might let a baby nap in it if it was on a firm surface and I was sitting right there the whole time, but even that would make me nervous to be honest. We have co-slept with all of our kids for years but are really safety conscious about it. For co-sleeping what about something likehttp://www.babydelight.com/
We ended up putting our mattress on the floor and moving the preschooler to a separate sleeping space on a crib matress right next to ours, so that was one less moving in the night factor. Not sure if that would work for you or not. All of my kids liked the slight elevation the Boppy provides, one of the parents would sleep on their back (we took turns) with an arm out to the side so we couldn't roll over, DC would sleep in that crook as a newborn with head on grownup's shoulder. Shoulder where DC could hear heartbeat was especially popular.
Congrats on the new little one. Sorry to be a killjoy about the product.