Ahhh both of your poor little girls, that makes me feel so sadfor a kid to be burdened with something like that is awful. Marcy, have you spoken to your daughter and asked what it is about vomiting that is frightening her so much? Does she know about your phobia?
If she asks you to sit in the bathroom with her, I think you're gonna have to muster every single ounce of courage you've got in your body and do it. This feeling icky, it's not because she's ill, it's anxiety and while it's scary for you too you just need to keep in mind that it's highly unlikely she'll actually be sick and just sit with her til she calms down and feels better and support her through it. Try and have some quite casual heart to hearts with her while you're sitting in the bathroom about how she's feeling and why and subtley put her at ease until her panic is subduing.
I hope you both manage to get your little girlies sorted out x