To answer concerns;
On falling love: My wife and I considered the "falling in love" part before we got into this. It came up as part of a discussion about having sex with a guy multiple times. We had been discussing that if you find a great guy to have sex with, then keep him around if the sex is so good. Why try moving on if you've already found great, unless you want more variety? Not that it's inevitable that a woman will fall in love with a guy she has sex with many times, but there's certainly a lot higher chance than if she has sex with him just once, right? We pondered that for a while, and decided it was probably ok for her to fall in love with another guy, so long as our relationship stayed primary. It's an absolutely false notion that you can't be romantically in love with more than one person at a time. We didn't feel her falling in love with another man would detract from us. If it did, if either of us felt like it was, then we'd pause things at least until we figured it all out. You won't know until you're in that situation exactly how it will work out for you. Is there risk? Sure, there's risk. But, if you love each other deeply and your commitment is strong, it's a very manageable risk.
On using this to get to have sex with other women: If your wife trusts that what you always tell her is the truth, then she should trust you when you say you're not doing it to get to have sex with other women. There's another aspect of this; most men feel that being honest means telling the truth when they say something. In my experience, this is true. It's also been my experience that women feel that being honest means telling not just the truth, but the whole story! It can take a lot of courage to tell a woman the entirety of the truth, and not just answer a question truthfully. Try it. See where you get to
On disrupting intimacy: Um, no, rather the opposite! Most couples report that on entering this lifestyle it dramatically sparks their sexual drive for each other. If it does disturb intimacy, then as with falling in love, pause things and figure it out.
On sin: Nobody can judge that but the two of you. I can tell you that for my wife and I, it came down to this; if it's a sin, where's the victim? Who is being hurt by it? If you're careful to protect your relationship (see falling love above), and you're not harming the guy she's having sex with by some means (example; he's cheating on his wife, his wife is being harmed even if she doesn't know it), then where, exactly is the sin? The Bible places some very stringent standards on things we're supposed to do, and many (and I do mean many) of those things are not held to in the modern world even by ordained ministers. So consider what is "adultery". It's harming something, staining something, destroying something. Having consensual sex with someone doesn't mean any of those things. For my wife and I, it's enhanced our marriage, improved our intimacy, improved communication, and made us closer than I think we could have possibly achieved with out. Maybe we could have, I don't know. But, we made it that close in part because of doing this lifestyle. It's not for everyone, but it's worked for us. I can't judge for you if it's sin, but for us it's been the opposite of sin.
It's wonderful that your wife is concerned about damaging things between the two of you. That shows a great deal of devotion and caring, and interest in placing your marriage above all else. That's very important!
While your wife having sexual freedom might be good, an alternate suggestion: Make the first time she has sex with someone else with you there, so that she can _see_ your reaction, and _see_ how much you enjoy it. My wife wanted me directly involved at first. Doing so gave her confidence to eventually be ok with me just watching, and then not long after going on solo dates.