Well, that sounds like a tough nut to crack. Have you met Amy? Do you have any opportunities to talk to her?
Is your husband still meeting her (at a gas station) before or after work? It seems strange that she wants this kind of relationship with him, has she said why?
I think it could be useful to write a letter to her, if you have some way of getting it delivered to her. I would suggest spend some time talking in this letter about your feelings and frustrations. However, have a care to be diplomatic in the letter, and not demeaning in any way. Even if you feel like lashing out at her, try not to do that.
Everyone does the things that they do for some reason, and sometimes it's a different reason than we thought. Increased communication with Amy might lead to an understanding with her that was unexpected.
For some reason, Amy is reluctant to meet at people's houses. She's reluctant to meet people in person. There must be something driving this reluctance.
It sounds like the situation is driving you nuts, but for some reason your husband doesn't seem to mind it. Why is he content with just chats at gas stations? If he is content with that, is that something you can live with?
"My husband says he is just going to let things ride and see where it leads ... He stopped putting effort into it also ..."
What effort was he putting into it originally? Has he said why that effort has stopped? What kind of effort would you like him to do? When you talk with him about the situation, what comes out of the conversation?
I'm just curious about the situation, because Amy seems to be acting strangely. But there could be quite a range of reasons for that. Heck, maybe she is just extremely shy and reclusive. But I won't assume that unless I know more about it. Could be some sinister reason too. Or maybe apathy is what's driving her. Or she's afraid of something.
In any case, more communication would be a good idea. Let me know what has been revealed by any communication so far. Hopefully your husband will at least talk about it, if Amy doesn't?
I hope I can be of some help.