FWIW, I don't think, unless they are very socially-inclined or you are at the end of your tether, that children of 2 need to have interaction with other children, other than at the park etc.
Please try not to worry. Worrying will make you tense, which may alter the way you deal with the negative behaviour (I'm not going to say "aggressive" behaviour, because that's too much of a label).
Pushing, biting etc is very common in children this age, and the reasons they do it are varied
-tiredness, causing a short fuse
-wanting something another child has, and not having the patience, or the language to ask for it (this apples to children, like my son, who had really good language at 2)
-hunger, causing bad temper
-what looks like aggression is actually a cack-handed attempt at making contact with a child, but the lack the social skills to do it gently
-biting can be caused by teething pain
-overstimulation - busy, noisy places used to get my DS2 over--excited and he'd start on his rampages
Then added to this, there's the fact that some DC's get a kick out of the attention an incident gets them, even though it's negative attention.
So my advice:
-Note carefully when things happen and why it might be
-Avoid whatver triggers it as much as you can - hunger, tiredness and over-stimulation - if a meltdown's starting, feed him or take him away from where he is
-hover if you have to. If he does something to another child, tell him "No hitting" firmly, take the toy away, take him away and make him sit quietly without looking at him.
-enlist the help of the staff in this - let them know you are concerned and try and come up with a consistent approach
-apologise to any parents of children he hurts, but don't make yourself a martyr. I've noticed the more you are down on your own child, the more some parents will take their cue and be judgmental about what is very common behaviour. Don't try and explain.
- speak with a low calm voice. Be firm but try not to be rough with him verbally or physically when you feel angry or mortified
Remember in most case this stage passes. It is horrible to be the mum of the "biter". It does not mean he will be a delinquent. DS2 was a nightmare but is extremely well-behaved. Basically, their self-control has to kick in and we can help that by having self-control ourselves.
Sorry for the essay