As a single mom, where I went my son went, I didn't have a choice. I'm one of 6, my mom made it very clear after we got grown that she had raised her 6, she wasn't raising ours, meaning don't think I'm your built in babysitter. She did, on occasion, babysit my son but believe me I didn't ask unless I at the end of my rope. That isn't to say she didn't love and spoil her grandkids, she did and even took me and my son to DW a number of times. I didn't take my son until he was around 2 1/2 but just because it wasn't on our radar until Mom moved to Florida, we honestly never even considered going to WDW.
As far as leaving him with someone else, um, read above.
As far as the heat in Florida, how do you think people who live in Florida deal with it? They certainly don't stay inside all day, we are from Georgia so that really was never a factor for us. Tshirt and a diaper, hydrate the little rats and go, have fun.
I was born in Cucamonga (wasn't Rancho back then) and I'm told I went to Disneyland almost from birth. Also saw the Rose Parade, don't remember either but not taking my brother's wasn't an option, so Mom and Dad took 6 kids, ranging from the age of 5 to just born everywhere (no family lived out there they were all back in Georgia). We went to restaurants, have pictures of all 6 of us on trips everywhere, lined up by height with the oldest brother usually holding me (he was 5 when I was born and I'm number 6, no twins, it was the 50s no birth control). Life doesn't stop when you have kids, it just get more interesting and, yes, on occasion a lot harder.