I am a teacher of young children and know it is common at this age for young children not to know how, or even want to socialize with others of similar age. You may want to get a book on child development in the toddler/preK years that explains this more in depth. Separating from mom dad or her primary care-giver to play with others is new for them. It is also difficult for children this age to share and even to initiate play with others at this young age, play is is a learned concept. Often children at 2-3 yrs prefer to play independently or along side others their age. They may communicate very little with playmates and are not yet ready for engaged participatory play. Sometimes toddlers just sit along side and play on their own, they enjoy playing on their own, but lilke to observe older peers at play while they sit along side. They are learning and are unsure how to initiate play, this is all normal development, so don't force things. They call this parallel play. As she gets a just little older she will be more comfortable getting in middle of play situations. You are doing the right thing by getting into play groups, take her to the park and kiddie pool too to expose her to other children her age as well as playdates with cousins etc if possible. It will get better mom. Good Luck