First off, the clip looks really great!
The mother is great, I love how she readjusts her grip on the seat around x210 on. Cool detail.
The baby needs a bit more love I think. What stands out mostly is when he swings his arms around at the beginning and at the end (love his business around x110 to x130, awesome). I would involve the chest and shoulders more during those parts. The arms feel a bit too separate. Think about how the arm swing will affect the shoulder and chest.
Same with his legs, they feel too IK-ish. Watch out for overstretching, like from x59 to 60. Areas like that feel too poppy. The toes are also pointed up all the time and there's almost no change in rotation during all the kicking. Babies don't have that much control over their foot rotations. So have them point up and then to the side as well and when the leg pulls back, rotate the foot a bit more down, so it's not always pointing up.
One last detail thing, your light pole disappears on x45.
Almost there, nice work!!