It's the latter with a hint of Lynn's inability to figure out how toddlers behave.
Panel 1: As Mike grabs on to Farley and whips him up in the air, Elly tells him to be gentle with him because he's a baby.
Panel 2: Farley's being a baby is also why he shouldn't pick him up so fast or run with him.
Panel 3: As she herself picks up Lizzie, she points out that babies need special care and treatment. You have to be extra nice to a baby.
Panel 4: As Elly saunters off to create a sign that says her house conserves water, Lizzie blows a raspberry at Mike over her shoulder.
Summary: Elly's message was "Don't manhandle the dog." What Mike heard is "We like Lizzie better than you."
ETA: I've been mulling this over for a while now based on what qnjones said in howtheduck's blog entry for today. Simply put, she says that Elly dropped the ball by not pointing out the crimson consequences of mauling the puppy. I happen to agree with her because it's better to be honest than be nice.