Between the ages of 2 and 3, children engage in “parallel play.” They play alongside one another but not with one another. They're not yet developmentally able to share toys, take turns, have conversations, and cooperate with one another. They're egocentric, don't understand that other kids have feelings, and are extremely possessive of their belongings. If a toy is snatched from their hands, for instance, they may scream because it feels like a part of themselves is being stripped away.
Parents at a park who implore their 2-year-old to share his toys in the sandbox and “be a good friend to the other kids” don't understand the stages of child development. Because of their unrealistic expectations, they can become easily frustrated by a toddler's normal behavior. It's not until children are 4 that they'll reap the benefits of a play-based program. At this age, they're developmentally ready: becoming less self-centered, realizing others have feelings, enjoying the company of other kids, and being able to communicate, cooperate, and work through conflicts.
Because of your son's current stage of development and limited speech, he could be overwhelmed by a play-based program. He might get easily frustrated and fearful in such an environment. His expressive (speaking) and receptive (understanding) language need to improve before he'll feel comfortable and in control in such a setting.
My son received free biweekly speech therapy sessions when he was 3 through our county's early intervention program. His speech therapists were phenomenal: kind, patient, knowledgeable, and extremely supportive to me as a new mom. I hope you have such services in your community and can utilize them for yourself and your son. Speech therapy is more effective when started earlier than later. The speech therapist may also have recommendations for you about playgroups and “Mommy and Me” classes.
You may want to read my article entitled, “ Why Parents Should Embrace Early Intervention Services for Their Child, Not Refuse Them.” https://wehavekids.com/parenting/Whats-So-Special-...