I wouldn't use the word trust so generally. Of course she trusts you. But does she expect that you will be there? Not exactly the same thing. Apparently, she has learned that you may not always be present when this happens. Brother seems to be. So, she goes there first. If you were about to vomit your stomach contents, would you go to the most reliably present person, or the one who is the parent? If they are the same person, then there is no issue. But if they are not...
I'm not sure how many committees you are on or how many boards and meetings you are required to attend. I, too, am a stay home mom, and my kids are 13 and 16. I've done my share of volunteering, and I'm sure my days of doing so are far from over. But... much of that volunteering involves my kids! At events where they are also present. Not meetings at night when the kids are home alone without me.
Perhaps if your husband is never home (your words) then you should make more of an effort to be home. From your post, it sounds like your kids view neither of you as ever home. I would want my kids to have a different view. My husband also works odd hours, and while he doesn't travel for his job, he has a long commute and often is not home until the kids are long since in bed, and is often gone long before they get up in the morning. This has been the case since they were babies. It's one of the reasons I AM a stay at home mom. For the stability it provides. Your husband is providing for the family, and I'm guessing his travel can't be avoided. But it sounds like your absences can be minimized. Easily. So I would do that.
Your daughter doesn't dis-trust you, but she can't rely on you to be there, either. I'd have a problem with that. And it wouldn't be with my daughter, but with myself and my schedule.
I'm sorry if it hurts your feelings. I'm sure your daughter is hurt by the fact that she can't expect you to be there when she needs you. Evidenced by the fact that she seeks her brother when she feels ill.