I agree with Wenda's explanation for why your daughter should be able to play with her friends without including her little brother. Your daughter and son are at different development places. Your daughter is ready and needs to learn how to play with friends her own age. If little brother tags along the friendship issue becomes more focused on their relationship with him. He can't do the same things they can causing their activities to be dumbed down. There will always be conflict because of their differences in ages and needs.
Aren't there other things that you let your daughter do because she is older that you don't let your son do? This is the same thing. We increase the amount of responsibility gradually as the child grows. Your daughter's tasks are to learn how to form relationships with same age kids. It is also to learn how to continue to grow in her relationship with brother. These are two different tasks. A part of her task is to balance her relationships. She can't do that with little brother hanging around. Little brothers really can be pests. I had 3 younger brothers.
When you insist that she always be with her brother she will be increasingly less able to play with him even when friends aren't around. She is no doubt already angry with you and with him. Our goal in parenting is to teach children how to get along in this world. As your daughter gets older, she may feel that she has to please; that she isn't able to decisions for herself about who she wants to have around her.
By letting her choose her activities with her friends she will become more adept at friendships. She will also feel less anger at her brother and be able to play with him other times. I suggest that if she has the choice she may choose to involve him some of the time. When the two girls are playing games appropriate only for someone with more mature social skills a little brother is unwanted. They would have to change their play to fit him in. Other times, such as bubble blowing, painting, hide-n-seek they can all play. Both of them need times separate from each other so that they can practice the activities that help them mature at the age they are currently in.