i think, if she wants to be there and you are confident that she can handle it, let her in.
obviously, it would be great if there could be some family member there to go with her if she decides she wants to leave, but that sounds not possible. so i think the doula suggestion is a great one. but make sure you are clear with the doula that if your daughter needs to leave, your daughter is her priority. the doula is typically there to support you and your spouse, that's why i suggest talking to her specifically about your daughter.
also, it wouldn't hurt to bring entertainment for her. i don't know about you, but my labors are long and booooring. a whole lot of hurry up and wait, esp if you aren't the one doing the work. bring a dvd player, coloring books, anything else that she can play with independently. bring her pillow and a blanket (and even a cot) in case she gets tired and wants to stay in the room with you. look into whether there is a park nearby or even on the hospital grounds. or a playroom in the hospital. so that she (with either the doula or your dh) can seek some diversion as needed. remember, hospitals can be boring for kids after a while. (they can be for adults, too. my dh and father will probably bring the xbox again!)
as for where she should be or how she can help, i suggest telling her that you need her help holding a leg or even holding your hand (though that seems less likely considering you'll probably need that hand for something along the way). something to keep her busy when you are pushing. my dad, when i was in labor with my first, chose to be at the head of the bed. he was there, but wasn't in the middle of it. even something at the side of the bed would be ok, but might be starting to get in the way of the nurses and such.
as for your dh. talk to him seriously about it beforehand. tell him that despite how tired he might be he needs to be there for both of you. he needs to be the bigger person, the father, and the husband. you can't do it all, he needs to help. sometimes appealing to his sense of "mr. fix it" or knowing that you need him will be enough to help him overcome his crankiness. and if needed, you might work out a signal ahead of time with him that tells him he needs to reign it in without getting into an argument in the delivery room.
it might also be a good thing to talk to your nurses and even your doctor. they will probably discourage her attendance, but you never know. one or more of the nurses might have some good ideas for ways she can help during the worst of it. it is worth a shot.
personally, i have a 3.5 year old. he'll be almost 4 by the time the baby comes. i want him there. we are making a family, and i don't feel like it will be complete or right without him at least nearby. we live 40 miles from the hospital we will be delivering in, so it isn't like home is right down the street. if we get to our due date, we will be induced in the hospital--that's the plan. but also, if we get to our due date, my parents should be here for the delivery and my dad has been given the task of keeping nate company and busy.
our ultimate goal, however, is a home birth. it is what i have planned with both of the boys and what we want with this pregnancy, too. if we go into labor before our due date we will be delivering at home. and that would be the best for everyone. nate can be at home, with his own toys and his own bed. but he won't have to be in the same room if he doesn't want to be. he can control how much he sees and is around for, so he won't get overwhelmed. hopefully. a hospital birth complicates it for us a bit because of our desire to have nate close by but not necessarily in the room. after 9 mos of prenatal appointments and numerous ultrasounds, i don't want him to miss the "big event" if he doesn't want to.
besides that i don't think keeping labor and delivery or birth a secret from kids is a good thing to do. no judgement for those who keep their kids out of the delivery room. none. but birth, just like death should not be a kept a secret. both are a part of life. but everyone has to decide what is best for their own kids.
hope this helps. good luck.