I don't see any problems in any of the two cases:
#1 - he has a valid AP and another one pending - that's a normal situation; you can file for your new AP before the current one expires. He's using a valid AP.
#2 - I'm suggesting either of the two - travel on H1, but get a stamp first or travel on approved AP - assuming of course both questions pertain to the same person, he _has_ got an approved AP and another one is pending.
What you cite from I-131 instructions is actually telling you this: if you file for AP and intend to use it, don't leave the states before it's approved or it's abandoned. Tk_tk _does_ have a valid AP and that's enough for travel. Only if your AP has expired or if you don't have one, you're not to leave US without approval.
In other words - your wife has AP pending and she cannot wait to get it, her former AP has expired, but she still goes to visit her mom in Croatia thinking that you'll send the AP document to her Croatian address once it's approved. That's a no-no!!! And that's what your I-131 excerpt warns about.