Christmas time can be a hard time to find airline discounts as the airlines know this is a peak travel time for most folks because kids are on vacation from school and folks are all traveling to visit one another on during the holidays. It is NOT generally a time when they go on discounts, but that is not to say that a discount can't be had if you are willing to be VERY VERY flexible on your travel days. In that way, you might find a cheaper flight. For example, possibly FLYING on Christmas Day and arriving on Boxing Day might make sense because in general, no one wants to fly/travel on those days so planes are all generally "lighter" on Christmas Day. Only thing, you might run into trouble hiring a car on Boxing Day but then again, airports don't tend to close and you can find that out in advance as to whether or not you could pick up a car on Boxing Day. It might be possible. If not, and your first night's lodgings are close to Shannon, you could always fetch a taxi or shuttle to where you are staying the first night and then go back to the airport to pick up your car the next day at the airport - just make sure you have RESERVED in advance so there is a car available for you when you arrive at the rental agency to pick it up.
Also, why are you looking at one-way fares? You can by r/t fares where you fly into one city and fly out of another city. One way fares tend to be VERY EXPENSIVE and if you can purchase a flight into Shannon and say, out of Heathrow to Florida for return home on one airline, I think it would cost you less than buying two one way tickets for everyone in your traveling party. Have you called and asked about that yet? Ideally Heathrow would be the easiest airport to depart for home from as they have the MOST international flights & airlines going in/out of this airport each day........it's huge. The next biggest airport is Manchester, which is north, and cannot compare by a long shot to Heathrow in terms of flight availability or airlines that come in and out internationally........HUGE, HUGE difference. You'll be wanting to leave for home out of Heathrow, where you can also hire and return your car, which is the "London" airport (though kind of outside the city) and the most accessible by all international airlines. Airport code is LHR.
I would start looking into Ireland/England combo fares and see what's available on prices and not wait too long to book. I'd also consider flying Christmas Day and arriving on Boxing Day (because nothing WILL BE happening on these days anyway) but FIRST CHECK IF YOU CAN RENT THE CAR and maybe consider flying on those days to see if it saves you money. My guess is that flying on Christmas could save you A LOT. Flying right up to Christmas might cost you A LOT because it's PRIME TIME and the airlines know it so they go for as much as they can get for each seat on that plane. Try some of the airline ticket discounters and see what they are charging. But directly through the airlines - you will be paying premium fares. It's just reality. It's called Peak Travel time and it's hard to beat.
Good luck, and be sure to check out our home page for fare sales etc. We keep an eye out for them everyday and so you never know what you might find here on FamilyVacationCritic.com to help you plan your trip. We look for deals for our members to help make trip planning easier. So don't forget to keep checking our site as well for discounts and deals frequently; we might find just what you are looking for - but together we can help get your trip strategically planned to save you the most money and make it fun, convenient and easy. BTW, the Ryanair suggestion above is a GREAT one for getting between Ireland and England so definitely use that idea......if it hadn't been mentioned, it's what I would have suggested as well. Great tip.
Keep us posted Bonita! We're here for you