Welcome to our forum.
Anything romantic that involves more than two people, that has emotional involvement (and probably some kind of commitment), and that all involved parties have knowledge and consent to, is polyamory (from my understanding of the term). Swinging is strictly sexual play and does not not have any emotional involvement or strings attached (except between the two members of the couple who are swinging together).
Swinging and polyamory can overlap by the way. For example, there could be a three-person poly group (a V or a triad) who also see people on the side in a casual sense. So, they're "swinging," even though they're also part of a poly group.
So, your poly girl, is she open to the idea of you dating other women? It sounds like that's a struggle for her emotionally, but she doesn't really want to make you limited in that area. How do you feel about that?
It's a central concept in polyamory that you can be in love with two (or more) persons, without wanting to leave either person. How does your poly girl feel about this?
She has a husband; will you and he be meeting up soon? Any chance of striking up a friendship with him? (Sometimes that helps.)
Sounds like you have a special relationship with this lady, even if there are still many fears and unknowns. I hope Polyamory.com can be of help to you in getting that all sorted out.
Love means never having to say, "Put down that meat cleaver!"