It's funny that I read this thread, as we just planned my daughter's first communion this weekend! Our date is for June, but around here, we are huge ethnic city, so churches, halls and restaurants book up quickly due to showers, weddings, baptisms and communions at that time of year.
We have a huge church, and have 3 weekends (Sat/Sun masses) in which to make private communions (during mass), with a small limit of only 10 children per mass, and then all chidlren must attend a huge ceremony on Father's Day. It is a very big deal around here - we are a very religious family, and so my daughter has been waiting to make her first communion since she was 2 years old! Each week at mass, she asks how many more days until her first communion?
That being said, I verbally let family know of the date, and then I send out invitations. I honestly don't get people who don't send out invitations - verbablly giving people dates just means trouble, and you can pretty much count on no one being there. People are just too busy to remember things without any invitation that can be stuck to the fridge, or, attached to a calendar.
In regards to attending, the concert is not a big deal at all. That can be cancelled, and in our family, it absolutely would be. The play is a bit harder, as that is a big commitment on the part of several family members.
I would ask if the date can be changed for the communion, but if it's like our church, it more than likely can't be, as all other dates are probably booked. If it's like our church, a child may only make his/her first communion during one of these weekends, and that is it. I would hope they would make a change for extenuating circumstances, such as death or illness, but this scenario wouldn't fall into that category in our church.
Good luck to OP in making this decision as this sounds like a very special event for her niece. Too bad the OP's sister didn't send out invitations, and too bad the OP didn't think to double check on the actual dates before committing to the play - that's how we do it in our family, and when it deviates from that, there are always scheduling problems.
Moral of the story - if you want people to attend, then you need to do whatever it takes to make sure that people understand the correct date.
Tiger