New poster, but frequent browser of these forums. Wonder if anyone has any ideas for me.

I have kind of a hellish trip coming up. The itinerary is:

Evening Aug 3:
UA DCA-ORD-CID

Morning Aug 4:
AA CID-ORD-FCO (Arr 7am Aug 5) [no status, but have miles to upgrade ORD-FCO flight if they'll let me]

Late night Aug 5:
AZ FCO-TIP

Meanwhile, my canine companion will be flying:
Aug 4: KLM IAD-AMS-FCO

Where I will pick him up 30 minutes after I arrive. Then, he becomes excess baggage and flys with us to Tripoli. The reason the AZ flight leaves so late is because it's the only flight that will get him to Tripoli without near-instant heat death. I hope.

So now I have a 14-hour day layover at FCO with a dog. Any good ideas of what I can/should do? Day room that he can be left in? Airport kennel? Will I actually be in customs for 10 hours trying to clear him (he has a chip, but I've never transited EU with him)?