I haven't done detailed comparisons, but I suspect you would be best off splitting this into two — a London Travelcard from Watford allowing you to travel to London and then spend the day on whatever London transport you require, and then tickets allowing you to get to your chosen airport.

London Travelcard

London Northwestern Railway, who operate many of the trains from Watford Junction station, offer a Family Travelcard product allowing for discounted travel into London for families. I haven't looked too deeply into it but I suspect this is your best likelihood of value here. Assuming you are going from Watford Junction station, this will cost £19 for each adult and £1 for each child, for a total of £41. There are no time restrictions on Sundays, though others reading this might like to know that on weekdays it cannot be used on trains arriving into London before 10:00. These fares should be purchasable from ticket vending machines and from the ticket office at Watford Junction. Your train from Watford Junction will arrive into the London Euston terminus. Your Travelcard will then be valid for unlimited trips within London Zones 1-9 on mainline trains, the London Underground, the DLR, buses, and trams; and also will allow you to buy reduced price riverboat tickets.

Fare to the airport

Since you'll already have a travelcard, you'll then just need to extend that travelcard to reach your chosen airport. None of your three listed airports are in the London Travelcard zones, so you'll have to buy extra tickets in each case. To extend a travelcard you can either choose to buy a ticket with the origin point being a station on the outside of the zones, or you can buy a special fare starting at "Boundary Zone 6". Some, but not all, ticket machines can issue these (try finding the "tickets from other stations" button), but mainline railway ticket offices staffed by a human certainly can.

For Luton

You want a fare from either Boundary Zone 6 or from Elstree & Borehamwood to "Luton Airport" — if you pick that destination specifically it will include free travel from Airport Parkway station to Luton Airport itself by the bus link (you may wish to check the situation if the Luton DART has opened by the time of your visit). This costs £11.50 for adults and £2 for children; it doesn't matter whether you get it from Boundary Zone 6 or Elstree & Borehamwood. The £2 child fare takes advantage of a Thameslink flat fare offer; without this offer the child fare would be £5.75. You might need to use a ticket office staffed by humans, or buy your tickets online, to get this fare. Thameslink trains to Luton Airport Parkway leave from many London stations including London St Pancras International, Farringdon, City Thameslink, London Blackfriars, and London Bridge. There are also less frequent fast trains run by East Midlands Railway leaving from London St Pancras International which run nonstop to Luton Airport Parkway, but I believe you will not be able to use the child flat fares on these so you'd need to pay the full child fare.

For Stansted

Because the fare zone numbers extend to 8 in the Stansted direction, and your travelcard from Watford is actually valid to zone 9, but Boundary Zone 8 fares are not available, your cheapest option here is to buy a fare from Cheshunt to Stansted Airport. This costs £12.50 for adults and £6.25 for children; there are no special discounts on Greater Anglia/Stansted Express for child fares to Stansted Airport. Trains to Stansted leave from London Liverpool Street.

For Gatwick

You want a fare from either Boundary Zone 6 or Coulsdon South to Gatwick Airport. This will cost £5.90 for adults. For children, if you intend to travel on the slightly faster Gatwick Express services from Victoria, you'll need to pay the full child fare of £2.95; otherwise there is a child flat fare of £2 (similar to as described in the "For Luton" section above) that is not valid on Gatwick Express but is valid on Southern and Thameslink services. I will also warn you that while this ticket combination (with the £2.95 child ticket) is certainly valid on Gatwick Express services, it is quite likely your ticket will not be accepted by the ticket barrier, and I have encountered quite a few clueless members of gateline staff in the past at Victoria who might take a bit of persuading before they'll let you through. Many fast services, some Gatwick Express and some Southern, leave from London Victoria station; and you can also leave from London Bridge, London Blackfriars, City Thameslink, Farringdon, or London St Pancras International (among other stations) on a Thameslink service if that's more convenient. The fare should be the same either way, and sometimes the alternatives can actually get you there faster than the Gatwick Express would.

For Heathrow

(For completeness I'll list the other two London airports as this might be relevant to others' interests if they have a travelcard)

Heathrow is in Zone 6 and thus with a Zone 1-6 travelcard you can travel here without paying any extra. However, this only applies to the Piccadilly Line and the Elizabeth Line; Travelcards are not valid at all on the Heathrow Express and so you would need to buy an entirely new ticket if you wish to travel on this faster service. The slower Piccadilly line crosses central London; the faster Elizabeth Line currently leaves from London Paddington station though this will shortly be extended to also cross central London. The fastest service, the Heathrow Express, also leaves from London Paddington.

For London City

London City Airport is in Zone 3 and thus you don't need another ticket to reach it. It is served only by the Docklands Light Railway.

Other notes

I assume you are combining this with a longer trip around Britain, or else perhaps you live reasonably locally, because otherwise I would say a day out in London is really not much time, especially when you are catching a flight the same evening. Just be aware that it's quite likely that even if you leave bright and early, in my experience you'll find you haven't made much of a dent in what London has to see by the time you need to leave for your flight.

You might also want to consider what you do with your luggage while exploring London. The Excess Baggage Company operates the left luggage facilities in many London railway stations. Be sure to get a quote beforehand as these can be quite pricey if you are used to places like Germany where left luggage lockers are the norm. There are other alternatives you could consider but these are outside the scope of this answer.