I am also a Sunday School teacher, and have been for many years. A few weeks ago, in Primary, a very drunk man carrying a large back pack walked in and sat down in the middle of the children's Primary service. It was scary and horrifying and he started behaving in a scary manner, standing up, waving arms shouting about Abraham Lincoln and all sorts of weird things. We had to get a few men to get him to leave. I didn't know if this guy was going to pull a gun out of his bag or what, I mean, it does happen, so I was ready to jump on him.
Also, last year a man from a local apartment complex came into the church, and molested a little boy in the bathroom, and a few years back, a teen girl was confronted by another person in a bathroom. We are a very open and friendly church and do not turn people away who are not members, but we have to be careful and protect the children at all costs.
For these reasons, we do NOT allow children to wander halls. Parents or a much older sibling (like 18 and up) must pick the children up at the classroom. Teachers stay with the child until the child is picked up. If a parent is very late, we will take the child directly to the parent. Children are not allowed to go to bathrooms alone. We get a Sunday school supervisor to escort the child to the bathroom.
I would seriously consider finding a new church. Especially 3 years old, he could be kidnapped, he could get lost, he could wander into the parking lot and get hit by a car. And really, a donut? No, I would not give my 3 year old a donut at church.
For snacks for the young children (4 and under, older kids do not get snacks), they sit at the snack table. We prepare snacks and bring them to them. They get a cup of water, and usually some sort of cracker, fruit gummies, raisins, banana slices... the parents take turns bring snacks so some of them are healthy while others not so much. We try and balance it out.
We have 2 hours of class time for children. It rotates between lessons, music time, and a large group lesson. For nursery (children 18 months through 3 years), they play, do bubbles, color and also have a music and scriptural lesson time.
As for toy hygiene, we do clean the toys with lysol and we got rid of soft toys that cannot be cleaned in that way, kept a few babies or soft toys, but bring them home and wash them. We still use playdough, but not very frequently.