How you get around it isn't the point really. It's how your wife thinks things through. Wrapping her brain about swinging is obviously hard. She is imbued with society's rules that sex is strictly a one-on-one thing, and that a married couple should never ever engage in sex activities outside of marriage. We're raised with this programming. It's drummed into us from an early age. Our society is filled with it. Anyone who ventures outside of it is (insert pejorative terms).
She enjoyed the other man playing with her breasts. That's great, and it may have planted seeds in her mind. But all you can do is open doors. You've opened many. But, you've had arguments over it. This is not good. I would encourage you to find a way to discuss swinging without it resulting in an argument, even if it's only slightly about swinging.
Also, specifically with regards to the other couple; are they swingers? Does the husband have permission to be playing with your wife? If not, the other wife may not be too pleased to see her husband playing with your wife's breasts. The other wife not being comfortable having sex in front of you and your wife is probably a hint that they are not swingers, and encouraging the other husband to play with your wife is not a good idea. This is a drama bomb waiting to happen.
Be mature, be adult. Discuss the September trip with your wife, and see how she feels about having sex in front of the other couple again. Don't layer anything else on it. Just sex with them watching. Don't tell her that you'll ask the other husband to touch her again, in fact quite the opposite. If she's agreeable, discuss it with the other couple. Be upfront about it. Inform them you and your wife would enjoy having sex in front of them again, and see how they feel about it. They don't have to have sex in front of you, just see how they feel. Maybe it can move up to having sex outside of the hot tub, in full view of them.
Your wife and my wife probably matched each other in their opinions of swinging ~5 years ago. Even 1 year ago, had I asked my wife she would have probably rejected it right out of hand. But 9 months ago, she verbally expressed it might be nice to have multiple men to massage her entire body at once. Since then, every step of the way has been a very slow progression. We talk frequently about swinging. We've never had an argument about it, but in general in our relationship we actively work to understand our disagreements rather than argue over them. Fast forward to now, and my wife thoroughly enjoys swinging. Just last night we were having sex and she was telling me how much she enjoyed her last swing partner and how much she looks forward to having sex with him again. Very hot!
It is possible for your wife to become comfortable with the idea of swinging. But, you can not pressure. Ever. All you can do is open doors. For my wife and I, one of the key things was understanding that the knee-jerk reaction against swinging was based on society's rules. I.e., other people were dictating to us how to live our lives. We do take counsel of other's advice, but we're not going to let them run our lives.