To be fair to the DH, we don't know that he isn't helping out with the baby. We don't anything at all about his side of the story- maybe he is still trying to flirt with her, but it's going right over head because she's exhausted? Maybe she used to be more alert when she got into bed, but now she's asleep as soon as her head hits the pillow and he hasn't caught on yet.
Maybe what she's calling suckling, he's calling kissing? I think that kissing your spouse on the shoulder and neck to get him or her in the mood is legitimate. Leaving stubble burns is going over the top, but it's possible he doesn't realize he's being so rough.
There's just too much that we can't know about the whole situation when it's posted by a friend of the couple in question who's only heard one side of the story. I still think that they way the woman handled it is just as bad as the things the husband is doing. creepy or not, at least he wasn't being mean spirited, and was trying to show his wife that he still loves her and feels attracted to her.
If she really wants to accomplish something she should talk to him calmly and rationally, and not snap at him and belittle him when he shows some emotion. Why are we letting her off the hook for telling her spouse that when he cries he's acting like a baby? That's inexcusable, IMHO. She should have said something when this behaviour first started, and not waited until she was so frustrated she snapped. Husbands are not mind readers, and it sounds to me like he's trying to renegotiate their "scrabble" routine now that the baby is here. She needs to participate in that negotiation, and if that means letting him know that it needs to be less often, or letting him know what she likes him to do, then she should do that. The point is, she needs to let him know, and not snap at him when he hasn't guessed right.