Hi M.---I agree with diluted juice, at first, and no milk. Milk is constipating and highly allergenic, being one of the biggest risks for developing type1 diabetes. Please go to www.pcrm.org, www.strongbones.org and www.notmilk.com to learn why cows milk is for cows and not for humans.
For the constipation issue, please offer her fiber rich foods. These would most likely be lots of fruits and veggies, which have lots of water in them. I work with a Naturopath who has her PhD in Nutrition and I have lots of info from her that I would be happy to share with you. I would also recommend going to www.askDrSears.com. I know they have advice on MANY subjects and an area where you can ask questions as well. The senior Dr. Sears has written over 30 books on child care. I highly recommend the Family Nutrition book and The Healthiest Kid in the Neighborhood.
I also recommend looking into a high quality whole food based supplement. I have the pleasure and honor of working with the same company that Dr. Sears works with. The supplement we both use contains the juiced and dehydrated food powders of 15 different fruits and veggies and the bran of 2 grains. It comes in gummies and has enough fiber in it to help things in the digestive system move, if you know what I mean.
Make a game out of drinking water. Maybe have her drink at least 4oz of water before she can drink anything else. I might even try offering her Fiji or Evian waters. These have a nice balance of minerals in them and do taste totally different than other bottled waters on the market. Yes, more expenseive but healthier as well. At 4, your daughter should be able to know the difference between simply not liking something and not liking something but drinking it anyway. Tell her that sometimes we have to do things that we don't want to do, especially when it is something that is good for us. But, appeal to her vanities. Does she want to be a ballerina? A model? A star soccer player? Tell her that lots of water is necessary to achieve these goals. I might also go get some books at the library that talk about the importance of consuming adequate amounts of water.
You are the mom and have to be strong. We have to teach our kids what they need to know, and drinking water is one of the most important things that we can do in order to achieve optimal health. I have tons of resources to share so feel free to contact me if you have any additional questions. Good luck, be well. D.