I'd definitely advise staying near the parks. The parks involve a lot of walking and it can be a tiring day for adults, and obviously doubly so for young children, so you won't want a long drag back to the hotel. Plus the fireworks at night are amazing (and a must see) but they're not until quite late, and if you've been all the park all day you're not going to want to wait around until nearly 10pm for the fireworks. If you are in a nearby hotel you can go back there at 5pm or something and then pop out again to the parks in the evening once you've rested your legs. Also the weather in April can be unpredictable so you may decide if there's a heavy shower that you want to be able to pop back to the hotel to dry off or escape the rain.
The main Disney hotels all provide free shuttle buses to the parks and are the closest places to stay, but they're quite expensive. They will though tell you that as a hotel guest you will get 'extra magic' hours as a Disney hotel guest, so you may feel this justifies the cost. However, how useful these are to you depends on how early you intend on getting up in the morning as (if I remember - I've not been for a few years now) the extra magic hours are between 8-10am, so not of much use if you don't plan on getting up early. A slightly cheaper option which I've done before is to stay here: www.explorershotels.com/en/ which is also very close by and done in a very 'themed Disney-esque way' but without the huge price tag. Loads of free shuttle buses from here too. Bear in mind that both the Explorers hotel and the main Disney hotel operate a 'time slot' system for breakfast, where they stagger the arrival at the breakfast buffet by giving you a set time to arrive for breakfast, so you don't have the freedom to just turn up for breakfast when you want.
As for how long to stay for, there are two parks there: Magic Kingdom and Hollywood Studios. There's also the Disney village which isn't a park, but a collection of Disney shops and themed restaurants just outside the main parks. Obviously your 4 year old won't meet the height restrictions for several of the big attractions, so if you are planning on just skipping these attractions altogether I'd say 3-4 days would be plenty, (3 if you are happy to just see most things, 4 probably if you want time to do pretty much everything and maybe repeat a couple of favourite rides). If you are still planning on doing some of the big attractions bear in mind these tend to have the longest queues, so 4-5 days would be better.
Not sure what else to advise apart from wear comfy shoes (as a say, lots of walking and time on your feet) and I'd probably say wear layers in April due to the unpredictability of the weather.