We have a 24/7 Adoration Chapel in our parish.
Many people bring their small children, but for only a few minutes. That’s precious! They usually point out Jesus to the little ones, teach them to kneel, perhaps say a short prayer with them, and then they leave. I heartily recommend this. I’ve done it with my nephew.
People do bring their older children for the whole hour, and often these children read books about Jesus, or pray, or just sit quietly. I think a lot of these children like being with Mom and/or Dad as much as they like being with Jesus.
I agree with many on this thread who say that the chapel should be kept as free of distractions as possible. As dear as babies and little children are, they are a distraction, even to people like me who don’t mind noise during prayer. You do not know the life situations of those who are in the chapel. Some people come because they are seeking solace and peace during a terrible time in their lives. Perhaps they would be encouraged by small children, and perhaps…they would not. I think most people would be encouraged by a small child and parent making a short visit to the chapel, but to have a small child fidgeting for a whole hour could cause someone to become upset and distracted away from Jesus.
I’m pretty certain that in the instructions posted in our Adoration Chapel, there is one that says that small children should not be allowed to make noise in the chapel, or should be removed from the chapel if others are present. Something like that–it’s phrased diplomatically, but the message is that this is a place for silence.
We have groups of homeschoolers who come to the chapel, but they sign up for an hour, and usually there are no other people there when they come.
If you don’t want to leave your children with a sitter, consider coming to Adoration in the middle of the night, or very early in the morning (at 3 a.m.), and leaving your little ones sleeping at home with their daddy in the house.
You asked about greeting the others. I nod, smile, and sometimes wave. If I know someone in the Chapel who is going through a hard time (death in the family, etc.), I will give them a “shoulder hug” to let them know that I care. But I don’t talk to people. Sometimes people try to talk to me, and I nod and smile, and whisper a few words, but nothing else. It’s not the place for this kind of thing. If the person seems to want to keep talking, I will gesture for us to go outside (as long as the chapel has others in it to keep Our Lord company).
One more thing–yes, most people do a complete bow (double genuflect). But many of us haven’t been able to do a kneel-down bow for years! My knees won’t allow this–sometimes just getting up from a seated position is difficult–so I just do as reverent a bow as I can. No one is expected to hurt themselves or get themselves into a difficult situation (unable to get up!) in the Adoration Chapel.
Enjoy being with the Lord!