First off, I know you address infant eating and sleeping questions all the time, so feel free to just direct me to a previously written column, etc.
She wakes up happy, but she is tired again after a little over an hour. But there have been times where she will sleep two hours or longer if I'm holding her (which I have stopped doing altogether for her naps). Your child is waking up after reaching the light sleep portion of a sleep cycle.
The potential benefits of infant sleep for memory processing are largely unexplored.
Here we show evidence that having an extended nap (≥30 min) within 4 h of learning helps 6- and 12-month-old infants to retain their memories for new behaviors across a 4- and 24-h delay.
I have a short nap routine and I use a sound machine during her naps. If your 4 month old learns to fall asleep independently through some form of sleep training - the level of crying sleep training needs to involve can be up to your family - then it may solve this problem.
The drive to sleep is much less during the day so it is more difficult for infants who do not fall asleep on their own to make it through a sleep cycle transition.