I was predictably dismayed to read about the situation with your 13-year-old daughter; her fear and now, her anger that has come between you. I've never pretended to understand the minds of young females and although I'm a parent, we had a son (now 30) who was a good boy and grew to be a fine young man, although of course, we had our issues during his adolescence. By the time I received my AN diagnosis, he was 27 and because I wasn't panicky (my wife wasn't quite so sanguine) he took my cue and treated the entire process; numerous doctor visits, multiple pre-op tests, the 9-hour surgery, 5-day hospitalization and - fortunately - a rapid recovery, with remarkable equanimity. I can't imagine how he would have reacted at 13 and if we'd had a pubescent young daughter, well, all bets would be off. That said, I offer you my sympathy - but no substantive advice. It's unfortunate that your daughter believes you could die from your AN, which, as we know, is technically true - but the chances of that happening are truly infinitesimal. However, I doubt statistics would carry much weight when a girl is convinced her mother could die - and leave her - because of a small, benign, partially excised skull-based tumor. It appears as if your daughter is struggling with her fear of losing you - and that fear has to be respected, even when it's practically baseless. Just as we sensitively deal with non-existent 'monsters under the bed' when our children are toddlers, we have to treat these fears of a 13-year-old girl about her mom dying as both real and somewhat serious.
I can't imagine your daughter growing up to be maladjusted over her misunderstanding the risks of her mother having an acoustic neuroma and subsequent removal surgery, back when she was 13 years old. However, I'm well aware that some children may carry the fallout of such incidents with them and later develop unhealthy attitudes because the issue was never properly addressed. Still, I'm 'old school 'and so, don't automatically fall back on 'therapy' and 'counseling' for every traumatic incident in my child's life, although I have no problem with these disciplines that help many. My son always had a good relationship with his mother and me. We talked. I was careful to treat him age-appropriately, that is, I didn't 'talk down' to him but I didn't expect him, at, say 13, to have the discernment of an adult, either. He went through some struggles during his adolescence and did see a doctor at one point (to determine if he had any physical problems) but for the most part, we muddled through and he did just fine. Today, we have a very strong bond.
I know that offering advice on child-raising issues is risky and fraught with too many opportunities to make enemies so I have absolutely no desire to give advice on a subject that I have only my own parenting experience to draw on, which is hardly impressive, I know. I have no expertise in this sort of thing so I'll simply mention that your daughter may well get past this on her own - or with her big sisters help - but I wouldn't make myself despondent and fearful of dire consequences to your daughter's psyche because you 'got sick' when she was 13 years old and unable to deal with her fears of 'losing' her mom. If professional counseling is called for, by all means, pursue that option. Whatever it takes. I can only hope and believe that your daughter will be O.K., in time.