@Bettyprime If you read my earlier post you will see that years ago, I was your DD13.
I struggle to put this in the right words so forgive me if I am clumsy. Your daughter knows she is loved, she obviously has a good relationship with you because she told you how she was feeling without any tantrums, falling out etc. You are obviously doing a lot right. I was also in a single parent family and I will start here by acknowledging that as a single parent, you are between a rock and a hard place.
A "glass child" is a term often used for a child who grows up alongside a sibling with high needs, whether that is due to disability, illness, behavioural difficulties, mental health problems, addiction, or simply a sibling who requires a disproportionate amount of your attention. The idea is that parents "look through" them like glass. Not because they don't love them, but because the louder or more urgent child's needs dominate family life.
The glass child often learns not to make demands, to minimise their own problems, to be "easy", to cope alone ant to feel unseen rather than unloved.
That's an important distinction. Many glass children will say: "I know my parents loved me." rather than "I felt important."
From your description and my own experience, what strikes me is that your DD13 isn't necessarily asking for more activities or more people. If a child says:
"Everything in this house revolves around my brother," the emotional message underneath is often: "Does anyone notice me?" rather than: "Can someone take me somewhere else for a few hours?". That is why some well-meaning suggestions can accidentally miss the point i.e. her friends coming around or more time with her Dad. Helpful if it is presented as "special time because you matter". Potentially harmful if it feels like "Mum stays with your brother while you go elsewhere because you are not her priority". More time with friends:
Helpful because every teenager needs peer relationships. Potentially unhelpful if the underlying complaint is about belonging within her own family and that is what she has told you she needs - to be seen and acknowledged.
The key question is whether she feels seen, heard and valued. For example, imagine two responses:
Response A
"Why don't you spend more time with your friends?" DD13 may hear: "Go somewhere else."
Response B
"I can see why you feel that way. Your brother does need a lot of attention, but I've clearly not done enough to show you that you're just as important to me."
DD13 hears: "I see you." Most children settle once they genuinely believe they've been understood.
What I also notice is that she's 13. That's an age where fairness becomes incredibly important. Teenagers are very sensitive to unequal treatment, and even when they intellectually understand why a sibling receives more attention, they can still feel hurt by it emotionally.
A parent can be completely justified in giving one child more time and still have another child who feels neglected. Both things can be true at once so please don't think I am getting at you as you have an awful lot on your plate.
So I would probably be asking: Does she get uninterrupted one-to-one attention? Does anyone ask about her day first? Are family decisions regularly altered because of her brother? When she expresses frustration, is she heard or immediately reminded about why her brother needs more support?
If the answer to those questions is often "no", then she may well be describing a glass-child experience.
My feeling, based on how you've characterised the discussion, is that your DD13 isn't necessarily looking for more distance from the family. She may be looking for more connection with the family and reassurance that she occupies an important place in it. Sometimes children who feel invisible don't need compensatory activities, they need someone to stop, look directly at them, and say: "I know things have revolved around your brother a lot recently. Thank you for telling me how you feel. You matter just as much, and I don't want you to feel overlooked." That sort of response addresses the wound itself, whereas sending her elsewhere only addresses the symptom. Sending her elsewhere without this reassurance will only reaffirm her feelings of being unseen.
You can never totally resolve this because you have a son whose behaviour can not be managed by a diary and you never know when you will need to prioritise him and ask your DD13 to understand, as it sounds like she does but understanding and feeling unseen are not mutually exclusive.
I think if you can an hour, sit down with your DD13, and tell her you have been thinking about what she has said and that you appreciate how nicely she said it. Tell her you love her and that you hear and see her and accept she is right but that it is out of your control. But tell her you can spend an inset day together, just you and her. Maybe see if you can get carers in or respite care for a weekend for your son - I think you could benefit from this too and you have a lot to cope with. Then spend some quality time with your daughter, try do this at least once a month. It doesn't need to be extravagant, just you and her time.
Big hugs OP, a says a lot that you have posted about it because you are not ignoring her, you want things to be better.