Costs will vary enormously as there are so many factors but as a family of 4 staying onsite at Disney and Universal for 2 weeks, we typically spend £10-15K all in. This includes flights, accommodation, park tickets, car hire, food and spending money.
I disagree that Disney is only for little ones. We have been going to WDW for years, first as a couple and then as a family. There is more than enough to keep anyone of any age occupied - with 4 parks and 2 waterparks. Universal has 2 parks and 1 water which are little more geared towards older children but not exclusively so.
Accommodation costs will vary depending on when you go and the type of experience you are after. An onsite stay is more immersive and convenient if you want to be close the parks. It can be more expensive but Disney has a broad range of accommodation to suit every pocket. Value resorts have great theming and are good for little ones but the standard rooms are very small and the amenities a bit basic. Moderate resorts in my view is a great compromise and deluxe resorts provide more comfort. For moderates, expect to pay between £200-3000per night and £350-500++ per night for deluxes in the summer.
It's not clear whether you have 4 children or whether your youngest is 4; this matters because this will impact on your accommodation choice. A few Disney hotels sleep 5 but not many (unless you want to pay for 2 rooms or a suite)
Offsite, there are a million different options - a villa in one of the communities in Kissimmee will provide lots of space, your own pool and away from the hassle and bustle and it can be more cost effective. It's been a few years since we did a villa stay but our last was a 4 bed in Cumbrian Lakes which cost us £1400 for 2 weeks in July 2015. It's not the best option if you don't drive and the traffic to get to parks and into town can be considerable. There are also plenty of other hotels, resorts and townhouses that you can get at very reasonable prices in Orlando and the surrounding areas.
Park tickets are pricey, no two ways about it - we've paid £439pp for 14 day Disney ultimate tickets for our planned trip this year. In 2019 we paid £399pp. If you want to visit Universal, you're looking at around £250+ for a 14 day ticket, you can get it for a bit less if you go for a 2/3 day ticket but often the savings are minimal. Universal has its own onsite hotels - 3 of them (Portofino Bay, Hard Rock and Royal Pacific) will get you front of line access to most of the rides in the parks with your stay
Direct flights in the summer will be between £800-£1k per person but you can find decent deals if you are willing to go indirect.
If you hire a car, expect to pay around £300-400 for 2 weeks for a standard SUV but you might need a bigger car depending on your family size. You will also have to pay for parking if staying onsite at Disney or Universal and of course fuel.
Spending money depends on whether or not we stay on site with the dining plan (free or otherwise) or offsite. Our typical spend for 2 weeks (food, souvenirs, shopping, tips) offsite is £3k and £1-1.5K onsite.
Other experiences such as trip to Busch Gardens, Discovery Cove, SeaWorld, Legoland etc will be extra on top but in my view these are not necessary for a first trip. If you want to get away from the parks, you can do a few days in the Keys, Clearwater or Anna Maria island which have lovely beaches for a more chilled break. I would stick to either Disney Parks Only and/or Universal only to keep costs down.
Finally, Disney trips can become a very expensive addiction so think carefully about going down this route. Head over to www.thedibb.co.uk and forums more advise and information.