There is nothing wrong, in my opinion, with being honest about how exhausting caring for three young children can be. Especially alone. But it is fortuitous that your family are a great help. I know my brother and sisters are always relieved when they can get a break by charming me into babysitting.
I won't tell. Though if my sibling's children are anything to go by, they often grow out of being fussy eaters. Not always, but usually. So there's hope for you yet.