Babies are upstairs in bedrooms in their own packnplays with the door closed and are free to cry if they need to but once put into bed they are not gotten up till I decide naptime is over. That is one of the reasons once they move to a mat they are used to being put down and staying put till I return.
For the baby is he is doing a morning and afternoon nap then no morning nap or make it 20 minutes from 9-9:30. If you are out and about in the morning be sure he isn't sleeping in the stroller or spending too much time confined to stroller, saucer, high chair etc while others run around at the park, do lessons etc. He needs to be down on the floor crawling, cruising the furnitures or whatever to also tucker himself out to need sleep.
If mom is putting him down to sleep at night very early and he gets to sleep in in the morning then he may be getting too much sleep overnight and not needing daytime sleep. If he is cranky then he goes back into bed and stays there. If not cranky then he goes into one of those large play yards with toys and entertains himself while I do the same.