Not exactly, but I too have known people with other severe outdoorsy phobias. What happened to those I knew was they immediately got crazy panicky when even so much as in the environment where X might get them, even if X was utterly innocuous. (In one case, slugs.) It was as if they lost 50 IQ points and reverted to being five years old, bam. It's a startling thing to see from the outside. And while I generally don't suffer fools easily, in these cases, I could see the fear was so sincere and so overwhelming, I've always dealt very gently with them, even got one woman out for a short walk with me despite her terror, telling her over and over, any time you want to turn around, we will. She needed to feel in control; I could see that. Physically, they are like one big muscle spasm. The voice is high and tight. You can see them battling themselves, and I'm not sure why you can--the tight jaw, maybe, the darting eyes. It's like you can see she's ready to sprint away but forcing herself not to.
Most people react really badly to that freaked/childish/stupid panic, and that's to me one of the most interesting things about the subject. Most people are disgusted, angry, impatient. People who have to live with it get really ticked about the phobia. They force the phobic beyond her comfort zone and try to logic her out of it. That really doesn't help, but the phobic feels at some level she deserves being hated. Now there's awful shame on top of this wave of adrenaline.
One of my phobic friends was afraid of snakes and bought snake skins to try and get her used to at least that much. Your phobic might have bonzai trees or some similar talisman against it. It won't work, but it shows she's trying.
I don't know how old your character's child is, but an older child, even an eight year old, would have to take (and would be used to taking) the parental role, coaxing Mom along until the panic abated.