In the Country of Hearts, Alice thought of Dee and Dum as rambunctious little brothers. In the Country of Clover, however, they spend most of their time in their adult forms, and Alice is confused and embarrassed by her budding feelings for them. She's also worried that, at some point, they'll want her to choose between them. She likes them both equally and doesn't know how she could possibly do that.
The twins are fairly low on my list of favorite lover interests for Alice, for a lot of reasons. One, I'm not a fan of relationships involving a main character and twins – it comes too close to twincest, which I also dislike. Two, the twins are gleefully violent. Yes, a lot of the Wonderland guys are violent, but they don't all revel in that violence quite as much as the twins. And three, the twins are usually very child-like, even in their adult forms. I'd argue that it's actually a little worse in their adult forms, because the disconnect between their appearance and their behavior is so jarring.
As in The March Hare's Revolution, Alice once again finds herself saddled with love interests who say threatening things that are supposed to be romantic. At one point, one of the twins says “If you leave us, big sis, we might do something bad.” Of course, they're likely to do “something bad” whether she leaves them or not, because killing random people who try to enter the Hatter Mansion is their job.
Alice's internal conflicts about being attracted to the twins apparently weren't enough, so the story included Dee and Dum competing for Alice's love. It was a little odd, since, despite Alice's worries about having to choose between them, the twins themselves had previously seemed perfectly fine with sharing Alice. Their effort to get the best gift for Alice was still amusing, however, and worked out pretty much the way I expected.
This would probably have worked better for me if it had been more about friendship/family-building than romance, since that would have significantly reduced the squick factor. Parts of the story were actually pretty sweet. The artwork was also good, although I noticed that Shichiri's interpretation of Vivaldi was a little different.