Possibly a dumb question about flights

I've checked and have seen the approved route list on the DEFRA web site, and unfortunately, none of the airports in the US are anywhere near us (the closest, it seems, is Chicago).  Is it possible to fly a dog from here (Memphis) to Chicago, then on to Manchester?  Would it have to be two separate flights, or could I have one itinerary booked that has a layover in Chicago, but does go straight from Chicago to Manchester?  I'm assuming all that really matters is that the plane actually goes directly from an approved airport to an approved airport, but I wasn't sure if the *originating* airport matters.

And on a similar note, does anyone know exactly what happens to pets that have itinerary with a layover?  I hate the thought of our dog just sitting in her crate for hours in addition to the flights!

I haven't done this yet, but my understanding is that the originating airport doesn't matter--what is important is the flight that they come into the UK on.  I don't believe an airline would put your pet on a flight if it was not allowed to get into the country that way.

As far as what happens to them during the layover, I imagine that it varies by carrier.  I am going to fly Continental (the only airline that doesn't have heat restrictions).  They have a dedicated center for pets, and the people I have talked to there have always been really helpful.  They need at least two hours for a layover, and my impression was that that time was spent transferring the animals.  Continental keeps the animals in air-conditioned vans when they are not in the cargo hold.  The last lady I talked to said that if I wanted a longer layover, they could take my dog out for a walk, to go potty, etc.  I'm not sure how long a layover that would require.  I don't know what other airlines do, however.