If whole family is taking oath yes they will sit together. Otherwise remaining family have to stay in guest area. Which is only few feets away in same room.
For strollers it depends location wise. Normally space is tight and you have to leave the strollers outside the room. Make sure you have someone with you (who is not taking oath) if infant or kids start crying they have to take care and in some cases they have to go outside room. If no one with you as guest than you might have to take kid outside yourself and your oath will not count.
Oath ceremony total is about 45 mts to 1 hour. But all above are for only when you are actually repeating oath words behind citizenship judge that is only for 10-15 minutes.
Good Luck
