Is the baby having reflux or colic problem? Normally if baby has these problems need to be carried all the time to get the comfort. Otherwise, it is good to let baby to spend time on bed/floor. 4 months old should be able to play by himself already. For me, I prefer to let baby to play independently as baby need not to be entertained all the time and they can self-entertain actually, e.g. by playing with their hands and fingers. If your sister is too attached to the baby or the baby is too attached to the mother, in future it is harder to train baby to self-play independently.
Just to share, my daugther always want me to be by her side to play with her since she is a baby as I always cling to her too. On the other hand, I always give opportunity for my son to self play and now he is able to play independently for a long period without whining.