There's no right answer to this.
It's not only different for every kid and family, but can change per the funeral.
What hits me though is 2 things:
1) If gma is more concerned with how the children make OTHERS feel, instead of how they themselves feel... her opinion gets nixed.
2) If she's just trying to allay your fears of disruption to others / trying to let you know children are welcome and appreciated, then that's something to consider (I've lost a LOT of people, there are different vibes/expectations at funerals), but how much sway it would have would depend on the situation.
The playing in the cemetery thing is pretty normal/healthy in MOST situations. It takes the scary out of things and teaches that it's okay to still be happy/play. Many people view cemeteries as very sad places. The children I know who have lost parents split into two basic camps: those who love cemeteries / it's a place to share happy memories / play/ share difficult times... and those who are terrified and traumatized by cemeteries and completely shut down. If your stepkids (boyfriend's children? I;m a little unclear as to your relationship to them) are PLAYING at the cemeteries, that bodes pretty well for them forming a healthy relationship with death and memories.
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Per your add: No. I do all those things for nieces, nephews, neighbor kids I've nannied for, my goddaughter... kids who I've spent YEARS with, who have lived with me... and I have absolutely NO SAY in their lives. That's their parent's job/decision. I can offer my opinion (sometimes! Most of the time it's far far wiser not to)... but that's all it is. I have no RIGHT to my opinion. Not until or unless I am their guardian. Neither do grandparents, friends, babysitters, etc have any right to say how my son should be raised. Be very very careful here. A good rule of thumb is : Nanny (or Aunt, school teacher, friend of the family, etc.)? Yes. Those roles are similar. Parent? No. Most people like kids and want to jump in... that's VERY dangerous ground.