niece is a horrible brat

I'd just ask her if she thought her little darling's behavior was going to make her popular with her peers.  I sure wouldn't go anywhere with sis either.  If she asks why just tell her why.  That her kid is uncivilized and that life is too short to put up with that nonsense.

For the motel, make sure your sister understands that it is UNSAFE for her child to wander about unsupervised.  Even the nicest hotels can have guests who are perverts.  If she is running while being watched by her parents, as long as she is not being noisy and disturbing people in their rooms, or impeding others who may be in the hall, I see no harm.  If you are asked to watch her, and do not wish to, politely decline.

As for meals, give the child notice that McDonalds is not the only restaurant, and that y'all will not spend the entire trip catering to a single person, that it is supposed to be enjoyable for all.  It is possible that your neice has been taught that vacations and fast food go together, and therefore it is part of her expectations--just as McDonalds is obviously NOT part of your expectations.  Teach her how to compromise.

Wow, I wouldn't want to go anywhere with this child either.   I also wouldn't let my kids dictate where we eat.  What's wrong with a family resturant?   They still have nuggets etc.    I would talk to your sister and say, that the McDonlads made you ill last time and of you are to go again you would like to go to a resuturant.  It will be good for her daughter too, worst case secniario, child goes hungry.  She will eat when she's hungry enough.   But am I'm guessing your sister doesn't do the tough love sort've thing...

   My sis told me, just a week ago.  We were planning a family outing.   I suggested Mc.Donalds, she said lately it's been putting her on the tollet, how about the food court at the mall.  I said sure, more for us to choose from.  (Us parents decided, before kids even know were going anywhere)  Heck, were the ones paying, when their old enough to pay, they can choose.

   As for the running in the halls, and leaving the room... That would've ended our family trip.  I would've said, one more time.. I'm loading the car back up and going home.  (My kids know I follow through, so that would've nipped it in the bud)   I think I've watched to much SVU, that is soo unsafe

You know,  for years my MIL used to complain that I was too strict with my kids.

Funny, now I hear her bragging all of the time that you can take my kids ANYWHERE. 

I'd tell this child - at 9 she is old enough to grasp this - that you like going places and had always thought you'd enjoy spending time with her,  but her behavior has been less than fun for you to deal with.  Make her an offer - improve your behavior and we'll consider trips to other places.   Keep your tone very conversational and matter of fact.

She's nine - she can understand bribery.

You cannot change your sister's parenting pattern.  It is extremely unlikely that you will change the interaction between your sister and her daughter.  But, you may be able to change the pattern between her and YOU. 

If you aren't stuck with her any more,  if you don't want to bother then don't.  Just avoid her.  If you'd like to save her from some aspects of what her behavior will bring her in the future,  try reason.

I have a nine year old sitting in the room with me.  They CAN be reasoned with.  Treat her like you expect her to be rational.  She might surprise you.

Sounds like it's too late for your niece and her mother....but you can set rules for when she spends time with you and insist on compliance.  It sounds as if this child really needs an adult role model to set some boundaries.  Kids like boundaries and they like, believe it or not, the safety those boundaries represent.  They can depend on that adult, at least, acting consistently about these things and kids love security and consistency.

I've had nieces that loved spending time with me even though I was more strict than their mothers.  I think it was simply because they always knew where they stood with me and someone was in control and they didn't have to be....that is a scary but exciting thing to a youngster, to be in control.  Sounds like your niece is certainly in control of your sis.

These days this seems to be more common. I grew up on bases all over the world. We where taught from the get go you NEVER cross a line you NEVER go where you not supposed to and most importantly when a grown up said something you listened and did what they said.

I have seen kind yell at there parents out shopping!  If I had raised my voice to my parents I shurly would not have done it a second time. These days with the not spanking kids and the kids are equal to adults this is not getting better. Respect seems to be lost on so many. Self respect and respect for others is thought to be a bad thing.

Another reason I LOVE living way out here. My land no neighbors I do things my way..

I tell my kids when we leave the house

A  this is where we are going.
B  this is what i expect from you and
C  if anyone misbehaves we will stay home. 

this works well with my 8 year old and 4 year old but I make sure they have eatten before we leave its usually when they are hungry or bored they start to rub each other the wrong way.  I also keep small toys in the vehicle for them.