The larger cabinet is designed to fit an over the door ironing board and the frame of it can easily be clamped to the sides of the cabinet.
The smaller cabinet is designed to fit a folding tabletop ironing board with the board resting on the door. I think that if you used a set of folding shelf brackets you could support the weight, upside down for the brackets but they're strong.
View with even doors. Alternatively, you can have 2 door sizes to close at the center divider, this would likely use a single board as the door for the thinner door, 1/2" wider than the opening.