I would imagine it is fairly normal for a teen girl (she's what? going into 8th grade?) to want her space away from her 10 yr old little brother (who's going into 5th? Is that right?)
8th grade is pretty drama filled for a lot of girls. How do her friends treat their siblings?
I would not force them to play together. But you can encourage it gently. As far as "doing things together"? I don't know what you are trying to say. Do you mean like working together on chores? Do you mean like taking them to movies together? Do you mean actually playing together?
My son and daughter are the same age difference, but my son is older than my daughter (so the reverse of your situation). They are our only 2. So no other younger sibs. They get along well for the most part. Son is 15, and is really hitting the "I'm too cool to hang out with anybody in the family" stage. He's a little moody and grumpy quite a lot these days. But that doesn't mean he is allowed to be mean to his younger sister. He doesn't HAVE to do things 'with' her, but he isn't allowed to be rude to her. They aren't opposites. Totally different things is what they are.
But, they do chores "together" sort of. She sets the table, and he makes the drink glasses for dinner. He takes the kitchen garbage out and she puts a new liner in the can. Etc. They accomplish things as a team, but work independently.
Try to keep the things they must actually do truly together, fun things. And recognize that hormones are playing a role now. Your daughter may just be grumpy and moody some, and it's ok for you to call her out on that. Don't expect miracles, but don't allow her to be rude to family, either. Basic manners ALWAYS apply.
We have NEVER "made" our kids play together. They usually do so on their own as they see fit. Some days it is a lot. Some days it is not. They are different people with different interests, but they can still make each laugh and have fun. They have inside jokes between them. But she loves to curl up with a good book for hours or play on the piano. He would rather wander around outside or play video games/watch movies sometimes. Or re-build skateboards switching out wheels and such. To each his own.