NewHusband - regarding your wife's sex drive, like Magdlyn said, it probably had to do with cycling. I myself tend to have a pretty distinct cycle (at least, I've started to notice in the last few months, as breastfeeding the last baby is finally winding down) wherein during ovulation I want sex about 4 times a day for about half a week, then I have the whole pms emotional mess, and period, and then I'm really not that interested for a couple weeks. Which doesn't mean I don't have sex for those weeks, just that I'm not ambushing Guy out of a shower, before work, after work, etc
and it's usually him initiating maybe every few days or so. So I completely get how your wife might not know if she wants sex - basically, I will be all - 'meh' about it if asked during the not interested time span, but if something happens that sparks interest (either Guy doing or saying something that triggers it, or me reading erotica, or something) then I'm good to go. Maybe ask her if there are things that trigger her interest that you could do when you're in the mood and see if that doesn't get things going?
Regarding not being happy with her having sex with someone else I can see that being hard to work through - Guy is currently working through how he feels with me now dating Morp, and so far, Morp and I have not had sex, but I'd like to in the future. So I don't have much advice on that, just that, I'm glad she's willing to wait and move slowly with her OSO until you can work through your feelings on that and be more comfortable.