Definitely a trip worth taking, and not too much golf in a short period of time. The American Club is fantastic, and worth a see, even if you're not staying there...
There is a slight possibility that the 36 hole day might wind up a bit tight from a daylight standpoint, if the first round was a 5 1/2 hr brute. Since it's a Tuesday though, you're likely to be OK. Good to have the Whistling Straits rounds be the only ones those days...
Most consider the Irish course to be the weakest of that lot, so in one sense, it may be too bad you're finishing there. On the other hand, if you get up that morning and the weather's marginal, you won't have to regret passing on it...
In any event, it's a terrific 4-plex of public access golf, and you should enjoy them all. It'd be worth seeing the back tees at Straits, if you can, although I don't know if they'll let anyone play them....
Peter