I wouldn't worry about the clothing - I've been through both parks in short overalls and (of course) jonjons without anyone taking notice.

The care rooms at First Aid stations and the family restrooms work well for changing - bring a changing pad, though, for your own protection.

As has already been noted, the security guards are looking for weapons and illegal items - a couple Bambinos won't faze them.

Use regular diapers during the day - keep the overnights for at night. (I'm loving the Little Builders as daytime diapers these days).

Being at a kid-friendly event is not an issue - interrupting the experience for others is. You could even hug a character without issue, but I wouldn't recommend sitting in their lap.

Be on your best behavior - while a lot of activities won't raise an eyebrow, even the sound of getting a spanking will (and I've heard actual kids being spanked in WDW restrooms before).