From where I am sitting, you are way over-thinking this. I have kids with the same spacing as you, except mine are boy/girl. My son is 13, and my daughter will turn 11 just 18 days before son's 14th birthday.
I have never forced them to play together. They do so on their own. Like yours, they WANT to play together. Sometimes my older one wants the younger one to do things with him (go outside, ride bikes, ride scooters, whatever) and she isn't interested. (she is much more introverted than he is, he is very social). I don't force her to play with him. They work it out on their own. Always have. They have learned to negotiate with each other.
Sounds like you need to teach your daughters the art of negotiation as well. It will help them in their other relationships later on, be they social relationships or business ones.
I try really hard not to step in when they are negotiating their "hanging out" time. When they were smaller (he was maybe 5 and she was 2) I had to be a bit more involved, and I was. I explained to him how to include her and how it feels to be excluded. And I explained to her (as she grew and could understand) the same things. Even when they have friends over, they are not allowed to unnecessarily exclude their sibling, just for the sake of excluding them. However, that doesn't mean that everything they do, that the sibling gets to do also. They both would get a "lecture" before the guest(s) arrival, so that they knew how to behave respectfully to each other.
I think you can have separate conversations with the girls and explain things easily enough. Big sis, I know you don't always want to include your little sis in everything you do, and that's ok. It's ok to want to be alone or do things that don't include her. But be aware that she really looks up to you and loves it when you spend time with her or include her in what you are doing. So it is really nice when you DO include her when you can.
Little sister, I know how much you enjoy spending time with big sis, but understand that everyone likes to have time to themselves once in a while, and if big sister wants to do something on her own, that's okay for her to do that. It isn't to hurt your feelings, and really has nothing to do with you, but with big sis needing some alone time. You'll understand it more as you get older. Maybe you already like having time to think or just 'be' without someone else always right there. Your big sis needs that sometimes, too. When she is feeling that way, give her some space and find something else that you can do on your own or with someone else besides her. She'll be available later probably, and she'll let you know.
Mom, you don't have to "drop the hammer" (lol) and tell her "she isn't interested in you". That is so harsh sounding. And it just isn't true. She is interested in her, but only on her terms. And when little sister figures out how to negotiate, they can both get what they want. That's the real art of negotiating----everyone gets a little of what they want, and has to give up a little of what they want. But everyone thinks the end deal is "worth it". :)