I would get your toddler a kids backpack thats not too heavy for them to carry, and put their things in it.
I have an isoki nappy bag which is one of the biggest you can get of "nappy" bags, and its really very heavy with things in for one baby, let alone 3.

Oioi and isoki do large bags, or otherwise something form a luggage store may be a better option for you, Im just worried about how you will lift it? Will your partner be going with you a lot of the time, or will it be you and all the kids? If there will be 2 adults Id get 2 nappy bags for the triplets and a backpack for your DS