One way to help with social skills is to role play.
Children with autism want to socialize, they just don’t know how! So they engage in socially awkward behaviors such as pushing, invading personal space, stimming, etc. Instead of apologizing to the other parent, TEACH your child what they need to say to get the child to play with them.
You can work on these skills at home by role playing with dolls or action figures. Act out scenarios where one approaches the other and says something like “Do you want to play with me?”