When my babies would get constipated, I would coursly grind seeds and add them to the carrots--worked like a charm!
After you sort out the constipation thing, I would get your kid used to drinking water. Simply don't offer anything else. It may take a day, or two, but they will drink. Don't force it, just offer it. When people are thirsty, they drink. I don't believe that any child will get them selves sick instead of drinking water.