<human>: Can you summarize the given text in a few sentences?

Hi y'all! This is a little bit different situation than the standard cheating/lying/murdering stories here. 

Me (29M) and my wife (32F) are good friends with Mary (40sF) and her husband. We are all involved in the same church groups and our children all play together.  They have 4 kids as do we. 

Their 4 y/o girl Lily is having her 5th birthday. Mary spoke with my wife about the birthday party and said "We are planning a party for little girls and would like Annie (our 5 y/o) to attend". They are renting out a gymnastics center or something to that effect. 

Now, we've been trying to keep the invite on the down low, as our 6 y/o Mabel is a little on the jealous side...she still carries that middle child syndrome heavily. Mabel plays with Lily every Sunday and during the week sometimes, and considers her a friend. 

Well, Mabel found out tonight about the party and that she is not invited...and had a meltdown. Now, I am not very tolerant of fits and tantrums at all, but she was heartbroken. She feels excluded and that she is purposely being kept from seeing her little friend. She is completely distraught. 

I don't normally cave to kids demands, but in this case I think it may be reasonable to ask our friend Mary if Mabel could attend. My wife would handle the contact, but she is worried about sounding greedy or overstepping or imposing, as she is always very relationally minded in trying to keep peace and happiness within her circle of friends, and she's not one to rock the boat or be very aggressive. 

How should we approach this in a tactful way that respects our friendship but also conveys how Mabel is feeling?

Thanks.
<bot>: My 6 y/o daughter wasn't invited to a party for a 5 y/o but her little 5y/o sister was. She's distraught. How to broach subject of invite to birthday girl's mom.