I have a carry on bag that is large enough to fit all of my personal stuff as well as my babies - just because I don't want to carry too much. Don't forget, it is one bag PLUS the personal-type item. So if you have only on bag, the diaper bag can count as your personal item.
From SWA website:
Per TSA regulations, carryon items are limited to one bag plus one smaller, personal-type item.
The following items are not considered carryon bags or personal-type items and are not counted against the one-bag plus one personal-type item limit:
A child restraint device for a child who has been ticketed, who has a seat reserved, or for which complimentary, available space exists.
Assistive/mobility devices for individuals with a disability. There is no limit to the number of assistive/mobility devices a Customer can bring onboard the aircraft.
Outer garments or other wearable articles of clothing.
Food for consumption during flight contained in disposable packaging.
Walking canes or umbrellas.