Hi there. Sorry you are dealing with this with your child. Why the refusal to talk to someone about it? What would make her 'refuse'? I get teens, preteens and all the moody stuff that comes with that (have a couple myself) but 11 is too young to refuse something that mom says will help. So, I'd set it up anyway and have something fun for her to do after. I present to my kids the idea of a psychologist to be someone other than me that they can have cheering them on, give them ideas for overcoming different things, and are safe from the things that come with 'mom' which is my own fear, bias and emotion because they are MY kids! The other tactic is to tell her that it must not be that bad if she doesn't want help. My kids that are now a couple years older than her (13 and 15) respond very well to questions such as you don't want to see a psychologist because? leaving that open ended for their answer. And okay, so what can I do to help? And questions like 'what do you think is going on and do you have any ideas to make it stop?' You know . . .. the whole letting them try to come up with ideas, guiding them and making them think it is their idea type of thing.
I have a son with auditory processing disorder. It has many facets to it. Do you feel that is what you are talking about or that she is literally hearing things. Is there a history of bipolar or mental health difficulties in your family?
So sorry to hear of your predicament. I too have Bipolar 1 and really sympathize with you. But you must know, especially since your mother etc. has bipolar, that this awful illness often runs in families. And in your case with it so prevalent in your family, there is something like a 50% chance. You might like to check that out but it is very high. Also, bipolar disorder is becoming very prevalent in children, but something that can be helped with the right treatment.
However, I am pleased that your daughter has confided in you, that is a good start, surely? She certainly does seem to have some psychosis going on - only applies to bipolar 1 as you know, usually in out-of-control mania, but can accompany depression too. And somebody, whatever their age, needs a lot of help with this. There really is nothing you can do to help with her psychosis - as you know trying to convince somebody of a fast-held belief is of no use whatsoever. Only a professional can intervene with the appropriate medication. I believe in psychotherapy, having had a great therapist for the past 18 years, but know that this is not appropriate treatment for psychosis. Once again no amount of reality checking has any effect on someone with psychosis. So the answer is medication, which can only be prescribed by a psychiatrist (not a therapist or counselor).
I don't have any kids, but would have thought an 11 year old would have to do what you say, not make her own rules. Arranging a special treat afterwards sounds like a great idea to me.
Not to scare you, but you must also know that there is a very high incidence of suicide with bipolar disorder, particularly bipolar 1. This usually occurs when a person is starting to get some energy back from being in a deep depression. But in any case, you would be well advised to get your daughter some treatment now rather than later.