Yes, you CAN do all 4 parks in 7 days, if you want. Depends on your family, and your desires.
You'll always get a lot of people who say, "Ooooh, that's way too many parks, slow down, go for 3 hours in the morning, take a long afternoon break, and go back for 3 hours in the evening." Why? B/c that's what they're used to, and that's what their family does. Doesn't mean you need to.
You'll always get a lot of people who say, "Sure, no problem. We're up from sunup to sundown, going all day in the parks, no break, and we hop around all week." Why? B/c that's what they're used to, and what their family does. Doesn't mean you need to.
You'll always get some in between who say "We do some of both - real active on some days, real relaxed on others, but we do what we want to do." Why? B/c that's what they're used to, and what their family does. Doesn't mean you need to.
Are you catching a pattern here?
Do what is right for YOUR family, depending on what YOU want to see and do! The ones who do little, might tell you that you'll wear yourself out, or be real tired, or be real hot, or your kids (in your case, kid) won't like it. You know what? Kid(s) are more resilient than most people think, and often handle this a LOT better than the adults do! But here's the deal - do what YOU want to. You'll have some who do a lot, and might tell you that you're not seeing enough of the parks, that your not having as much fun as you could by not seeing everything, if you go to leisurely (I personally subscribe to this theory, and we have 4 kids, 2 under 3, who have been 3 times! But whatever...). You know what? Maybe you're more prone to heat exhaustion or being tired than those people. But here's the deal - do what YOU want to.
It's YOUR vacation, not mine or anyone else's. Is it possible to do all 4 parks in a 7-day trip? Absolutely, and you can do it and see most everything, and still not feel rushed. Do you HAVE to? No, there's no rules. But you never know how it is, until you TRY it!