Children have the same struggles as adults with their emotions, learning to figure out their feelings or how to express themselves. Also like adults, what works for one child may not be as helpful with another.
For some children, giving them time alone to process their emotions can be helpful; others will benefit more from verbal processing. Many grieving adults experience switching in and out of grieving emotions, sometimes seemingly randomly. For children, this means sometimes they will be totally fine to play by themselves, but then all of a sudden they will need support for their emotions and grief. A practical tip to support your child in this is to keep play dates shorter and at your own home. This allows your children those needed connections with friends but gives them the ability to switch back into their grieving when/if needed.
Teenagers often need time alone to process their emotions independently, which can be appropriate for their age range and personality, depending on the child. Parents are encouraged to keep an eye on the balance between isolating themselves because they need the time alone and reaching out to their family and friends because they need that, too. Be sure to support them during this time of processing and struggle. Try to be open about what happened as much as possible or appropriate, leave the door open for questions should your children have them, and create a space for love and communication in your relationships.
Also, please remember to give yourself the same grace you give your kids. Emotions are hard things for us adults as well. So make sure you take some time for yourself if you can and care for your own emotions as well. We cannot help our kids if we are burned out ourselves.