I think I'm running into a situation where I think I need to break up a relationship, because the living situation of my love and her partner isn't poly-friendly. I'm minimized when he's around, not allowed into their home, and having to hide the relationship when she and I are in her neighbourhood. I've tried to deal with this for a while, and it's up and down... my gut tells me I need to break up, purely because right now, the situation isn't fair to me.
I'm a big proponent of listening to your gut. But only you can know whether to act on what it is saying. Too often our gut acts hastily from our survival mechanism and this instinct can be faulty in our modern society. But in your case...
The fact is that non-monogamy, as much as we might like to think we know how it 'should' be practiced, is practised in many different ways across the world. Cultural and personal values combine in a myriad of ways to determine how. Your love and her partner seem to be expressing their non-monogamous inclination in a Don't Ask, Don't Tell paradigm. And as with all DADT paradigms, it is hierarchical and 'secondaries' have fewer rights than the primary - in this case recognition of you both in and out of the home, as a valid partner (and indeed human being).
DADT, whilst it may be open-ish, is mostly incompatible with polyamory - if you define polyamory, as I do - as a form of responsible ethical, consensual non-monogamy. Your ethics may include not treating a partner like a second class citizen. That's not to say some people don't accept this style, for their own valid reasons (and might even prefer it) but it doesn't sound like you do.
Polyamory also has a focus on trying to overcome emotional issues like jealousy, insecurity, and possession. It sounds like your love's partner may be experiencing these issues and is unwilling to deal with them. If you are inclined towards non-hierarchical polyamory as a relationship choice, I agree that this DADT situation will not meet your needs. Perhaps first then you might determine the reasons why he has set these rules. Perhaps his job, his standing, his children may be at risk if the relationship becomes known outside the home. But personally I hold out little hope if you're not even allowed into their home.
Do you know for sure that it's her partner who's the problem?
I don't think it is. The crux of the problem is that your love also adheres to this belief system - however much she attributes responsibility to him - and has bought into couple privilege (characteristic of DADT) of treating you like a second class citizen. And as you don't want that, I think breaking up is absolutely the right thing - for you.