I think this fits under the "every child is different" (developmentally, socially, emotionally) category, not necessarily that they are an AP home or only child, etc. Some kids don't care if there is an adult/parent close by, and others have a really hard time with this. Heading off to a totally different part of the house, out of sight, and expecting a 2 year old to be totally content with this is a big expectation.

You might need to either lower your expectations or alter how you do your chores during the day.

Having only two kids, expecially both under 3, can make it harder for them to keep themselves busy for long periods of time independently.