Ummmmmm....you do realize you are your mom? Your mom won't let anyone else stay with your kids? And now you haven't left your kids since they were born? And your mom insists that she stay wth them if you don't? And why is it that she gets a say in who YOUR children stay with?
Do your boys ever spend the night away? If they have friends that they have sleepovers with-send them over to those kids' houses for the weekend. Truthfully if there are sports involved or other weekend events-it will be easier for the kids to be with a team mate than having your mother figure out where that soccer/football field is.
I have been going on "girl's weekends" with my high school friends since before my kids were born-leaving my husband in charge. Once my kids were school age I would frequently have them stay with friends over these weekends-or at least for part of the weekend- because it was overwhelming for my husband to handle three kids and all of their events alone. The kids absolutely LOVE being with their friends-especially if it is a school night! And it makes your vacation also a vacation for them.
And if you feel your mom is the only way to go-those kids are pretty old. They should be able to handle themselves pretty much and Grandma should just be there "holding down the fort". If there are sports, etc to go to I still recommend having someone else's parents on the team picking them up and doing the driving. Eighty three year old grandma may still drive-my 87 year old parents drive-but she may get flustered at not knowing exactly where she is going. And sports teams are VERY big on being on time so my kids stress if we are running late.
Think. In three years that 15 year old will graduate from high school. Are you going to college with him? Is Grandma? He has to learn some independence sometime. And with cell phones, you can touch base with them daily. I truly believe we over manage our kids. I see that I have done it with my own and am now trying to undo some of the "mothering". They can actually be very independent and proud of themselves-but not if we do everything for them and never let them put on their own.
Have a GREAT trip.
good luck!