"And I can hug him and squeeze him and pet him..."

Bunners

Well, who wouldn't want to hug or squeeze or pet that cute ball of fur?^^

So, why the tears?

Is that Carmen's child, after her death or something?

Yep, he's the father Carmen is the mother and I probably should've explained more in the description (curse my laziness^^):
Carmen and Wolf as children grew up as friends, then as teenagers they started dating. A certain event, however, led to their breakup and they grew apart. Years later they slowly rebuilt their friendship and after an unplanned night of passion and (nine months, during which that stupid wolf managed to break her heart (again)) Carmen dies during childbirth.
Now, as to why he's crying, possibly because the cub's resemblance to his mother reminds Wolf of the one girl he ever truly loved but also lost. Or maybe deep down he feels that his breaking her heart was responsible for her death. Or perhaps he's torn between the feeling of fatherly love and the fear of being an unsuitable parent to his pups.
Hope that explained everything :)