To illustrate further. The mothers all arrive anxious, already hoping that their child won't decide to have one of their (human) "moments". The children are probably dressed a little better than their "normal" wear (as they have to make a good impression at the group). And they are most likely uncomfortable from being rousted out of their "usual" routine to attend. Suddenly they are exposed to several toddlers, close to their own size, all cramped into a small space and there are just as many nervous mothers hovering over them.
In looking at it from this viewpoint, it seems like a place where stresses are just WAITING to happen, doesn't it? Take it from an experienced parent toddler leader who later resigned, it is a stressful place! When toddlers are stressed they often misbehave and exhibit bullying behavior. This is because they do not have the skills yet to "be nice", understand "sharing" and so forth. The bottom line: they are not ready for this controlled environment.
As important as I think it is to make contacts and be social and have friends, the idea of having a set block of time to over stimulate a very young child seemed very unnatural to me and in my observation, does much more harm than good. The main goal and reason for these groups is to have the mothers meet one another and exchange ideas, thoughts, etc. The toddlers are too young to be expected to share and to "socialize" for a 2 hour period.
A much more realistic situation would be to meet at your own convenience at a park, go on errands together, etc. with the children along of course. In this way the child is not placed on display and not (what I like to call) pre-stressed with comments (which the toddler hears as expectations) such as "today we are going to the new playgroup... lots of other children will be there" and so on.
A toddler longs for rhythm, repetition and activities which feel safe. As a parent, you should continue on your daily rhythm or schedule and then slowly add a child, or two, or three within your daily activity. Contact other mothers while your toddler is napping and arrange a play date at the park, or some other place where there is freedom to move about and nature or animals to explore. They key is that this is a natural event.
Being a part of regular activities which the child is used to is calming to the child. The mother doesn't need to feel stressed that she needs to make a certain appearance and that she is "locked in" to a set period of time. This makes everyone a lot more comfortable, and when you are more comfortable and stress free, you enjoy the time more.
Up until about 20 years ago, most children this age spent all of their time at home with mother and siblings. Play dates and groups are a relatively new concept. The age appropriate behavior for a child this age is to observe and learn by modeling YOUR behavior.
Toddlers don't want friends, they want to do what you do! They enjoy hanging on your hip or standing along side of you doing the dishes, the laundry, going to the market, etc. These daily activities are learning experiences and a joy for children of this age to participate in.
Reassure yourself that there is plenty of time for friends later. They will have the rest of their lives to socially interact with other children, and in a few short years, they will rather run off to play with children than to spend time at your side. Don't worry about your child getting socialized. The same way they learned to talk and walk, they will learn to play and be social.
My guess is that what the toddler who is being a bully is trying to say to his mother is this: "TAKE ME HOME, I'm too little for friends!"
An excellent book which I highly recommended is Parenting a Path Through Childhood by Dotty Turner Coplen. This book helps parents by answering the following questions: "WHO is a child?" "WHAT is a parent?" and "WHY does a child only need a parent in the early years?" More importantly, it leaves all of the dogma behind and brings the reader to the reality of daily living as it should be.