Don't expect the same routines, while you have the combined summer time together.
Will this be in your house??? Or they live nearby you and thus that is what you mean by "we decided to spend the summer together..." or are you all taking a trip together?
It seems stressful when, as you said, both families spend extended time together. So, is the spending the summer together, a "have to?" Or you don't have to?
Next: your kids are 6 and 9. AHEAD of time, and before you are all combined... you NEED to sit your kids down and have a conversation. I do this with my kids all the time, they are 5 & 9. But anyway, TELL your kids and EXPLAIN to them, that all families are different. They should know that by now. And that, just because other kids are doing something or eating something or acting a certain way... it does NOT mean, that it is "okay" or "correct" or "better", than them. And stress to your kids... that they are their own person... and that being "followers" just because other kids are doing something, does not mean that they "copy" and that others... think for them. THEY can think for themselves.
Teach them that people live differently... but that they think for themselves and per how you are all a family.
You teach, kids that. I've been teaching my kids that for awhile now. So they can think on their own, and make their own decisions. Not just by majority rules or by what other kids are doing. Because, that is not always the best way.
Anyway, well you all decided to spend the summer together.
So, typical routines, WILL BE, affected. It is just a given.
And, just because you don't let your kids drink soda... it does not make you a "mean" Aunty or parent. I don't even let my kids drink soda.
But again... you all decided to spend the summer together... so, your rules for your kids/family will be affected... it may be irritating, but the loosey-goose relatives/kids... will be the ones that will seem "funner."
But so you tell your kids, ahead of time... they may be allowed more leeway... BUT it is not permanent. It is just special. BUT... they NEED TO ASK YOU FIRST. Just have manners about it... not just being rude about it. And to mind their manners. Not be cave-men about it. LOL
If they are respectful, and they have manners about it all and ask you first politely and show some respect for the fact that they are allowed to do things/eat other things like their cousins, then at least be nice about it, to Mommy.
Have a talk with them, BEFORE all of the combined-summer-together happens.
AND MAKE SURE, that you explain to your kids, that this is NOT permanent. They STILL have their same routines at home.
Whether it is a loosey-goosey family and their influence, or influences at school with other kids... you TEACH your kids... that being a copy-cat is not the "smartest" way. So that they can think for themselves and DISCERN situations.
You cannot, just keep to only your routines, when you are all together. It just ain't gonna happen.
But so have that talk, with your kids.
That is what I do.
And my kids understand.
The problem you have is:
They make you out to be the "mean" Aunty/Mom.
And your Sister and the rest of the family, call you too "rigid."
And the other problem is: that you ALL agreed to spend the summer together. I would not do that personally.
Is this going to be every darn day???
No one will be able to relax, and it seems "you" will be the one to keep things organized. Not your Sister. She is not parenting. And yes, you WILL have to pick up, HER SLACK.
Seems like a vacation for your sister, and you babysitting your AND her kids.
Not fun.
I would not agree to spend the summer together.
I personally, would NOT want to spend, every darn day, 24/7, with them.
I would go, crazy.