Congratulations that you have a baby on the way!
That pattern book looks like a nice one. I like the cover items.
It's always tight to work more than one stitch at the same time. I normally knit continentally, but that takes a fair amount of room in the stitch to work it. When I have to do a k2tog, most of the time I end up "throwing" the yarn (like English knitters do), because it makes a tight stitch like that easier to work. For purling two together, I work it my usual continental way and it works fine. I'm not sure I've ever done a pattern that requires p3tog! I can see how that would be tight and tricky though! Especially the second time, with the extra yarn in it from purling it the first time!
Good luck finishing it in time for the baby! I hope we get to see pictures: of the blanket AND the baby!
Happy knitting and Happy New Year!