I have a few thoughts on this that I feel like sharing.
I have seen many people choose fluid bonding only for their spouse(s) or long term live in relationships, and it can have to do with safety issues, with feeling special, with pregnancy worries (real or imagined). I don't know that she needs to give you reasons you think are valid that she doesn't want her husband to stop using condoms with you. I don't think pressing her on it now when she's said she isn't comfortable about it would be the kind thing to do.
When I was married previously, I started dating a person who had (partially imagined, mostly self created) ED and performance issues. It was my first other relationship that got serious, and condoms were making it very hard to have intercourse. I asked my husband if I could stop using condoms with this partner after 6 months. I knew it was pushing his comfort to do so, I knew I wouldn't appreciate being asked the same so soon, but I wanted to make it easy on my other partner, and I wanted to be having sex with him whenever we were together, so I did it anyway. I count that as the first of two times so far in poly that I rushed something that didn't need to be rushed, and put my SO in a bad position.
My current husband has issues using condoms (he's that guy up in the paragraph above I was talking about). We have had lots of talks about this, because even though it's hard for him to have sex with them on, we've agreed to not discuss fluid bonding with other partners until a relationship is long term, though we haven't set a specific "time". I don't imagine I'd feel comfortable with him fluid bonding with somebody for closer to a year. And I'd want to be friendly with them, and their partner(s) too, so I could really feel I had a handle on risk levels. I think that'd be the case even if we ended up in a closed quad. I do have to say I think there's a zero% chance I would ditch the condoms for him or for myself for a partner we weren't seeing much more regularly than 3-4 times a year, no matter how much he or I loved them.
My first husband to cheated on me after 12 years, the first time we we had a chance to have other partners (panic ensued after not finding anybody to sleep with so he made a bad choice so he could have a "sure thing") He did everything wrong including not using condoms. I never in a million years would've believed he could do that. If your partner's wife has ever been cheated on, expecting her to really trust acquaintances with her life (cause that's how I see it) no matter how trustworthy you know you are, no matter how much you trust your husband, that's asking a lot.
I also imagine that if she isn't feeling a lot of compersion with him dating you, the request to start trying condoms with him to help make it easier for him to have sex with YOU might not be met as a positive. It's something I want to practice with my husband because I want him to be able to have awesome sex, but I can certainly see how it could be viewed negatively, so please don't be offended if she doesn't jump eagerly to help. If they have any sexual issues at all themselves that could compound their problems too and cause resentment.
Anyway, I understand the frustration. I urge you to give her as much empathy and space to get comfortable with what you want as you can, as she is monogamous and we know there are a whole set of additional issues in mono-poly relationships. Since you are his first other sexual partner, it is probably all sorts of stressful for her, and there's no actual reason not to take it slow, nobody ever died from not getting to set asides condoms to have more sex. Just look at it as character building.
I can only imagine how threatened I'd be if my husband was plotting with another partner to break an agreement we had because he was tired of waiting for me to be comfortable enough so he could do what he wanted. I know you think you have good reasons, but if your husband started deciding he wanted to do things that you had agreements against, I don't imagine you'd be too happy about it either.
I kinda suggest you try to be OK with what you can have for another few months. Leave the condom talk off the table during your interactions, enjoy what you can, and let them work it out between themselves. Riling each other up with how unhappy you are and how much better it could be "if only" isn't doing anybody any favors I am guessing.
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