It is forbidden to touch food for no reason on Yom Kippur. However, if little children require to be fed, one is permitted to touch the food in order to give it to them. Wherever possible, the mothers should feed them.
On Pesah (Passover), it is forbidden to touch חמץ (Hames - leaven), because we are concerned that one may accidentally come to eat it. The reason why, on Yom Kippur we are not concerned that if they touch the food they might come to accidentally eat it, or drink the liquids, is because the fear of the judgment is upon them.
In the absence of the reason of having to feed the children, however, one may not touch food at all on Yom Kippur. In such a case we need to be concerned that one may accidentally come to eat from it.
(See Rama, 612: 10. Kaf Hahayyim, ibid., Oth 54, 44-46)
Yom Kippur, Yom Hakippurim, feeding children on a fast day