I don't understand why she would want a one-sided relationship either, but maybe she needs more experience/ needs to really burn herself to understand what she really wants. The hard part is, sometimes you can't help, just be there and bite your tongue on the "I told you" when people learn. Or maybe she IS into the chase...
I'd say yes, the metamour can choose to avoid contact (or the husband can choose to avoid contact), BUT many people do want a more involved dynamic. People still have to "get along on some level", but this can look very different for different relationships. There are many steps between "no contact" and "kitchen table".
Even "no-contact" metamours will usually be understanding and accommodating of each other's relationship and scheduling needs, etc., as communicated by the hinge. There could be a lot of respect and goodwill even towards a spouse you don't desire to meet. I think all my kink partners asked repeatedly how my partner is coping with the dynamics even if they didn't know each other.
A good basis (if, perhaps, you have nothing in common with your metamour) is "basic polite", where you're able to just talk for a few minutes between the door or invite them up for coffee when they come pick up your wife or if you happen to attend the same social event. I'd still call this "parallel poly".
There could be a friendly non-intimate dynamic, or when you're all ok watching a movie together, or the guys go for a beer sometimes, connecting over common topics, you invite them for birthdays, etc. Some people call this "garden party" poly.

You can intentionally introduce some functional elements into the dynamics, like bi-weekly three-way talks to check where everyone is, talk about feelings and hash out scheduling conflicts.
On a more involved level, you could still maintain separate living spaces, but be buddies, do sleep-overs or lunch, visit play events, meet each other's families, celebrate Christmas together or whatever. I think this is still really common, much more common than all the people truly living in one house or apartment.
In theory you could have a triad dynamic, where everyone loves each other, but it's often the most difficult to maintain, and those that happen spontaneously tend to have a better chance than planned ones - although there was a post from someone who intentionally sought triads and had some just yesterday.
Sometimes the level of involvement slowly progresses as the relationship(s) deepen. Sometimes all parties agree that getting to an arrangement where they can share living space is desirable, and work towards that, sometimes they seek alternative solutions even for committed relationships, like the hinge going back and forth between homes.
You can aim for any dynamics you want, but I'd say involvement needs to respect the slowest person - which could be you, your metamour or even your wife. (Although it's more common for the hinge to want everyone to get along great and share space.) It sounds like she's now at a point where she desires very separate relationships.