Hi M.! I only allow one cup of juice a day for my kids and have just made this a rule. .. it took awhile, but they know the rules and are fine with it. To get my kids to drink water I have been buying Minute Maid WaterFalls...I buy this in place of the Capri Sun Roaring Waters because Minute Maid is all water and a splash of REAL fruit juice and no additives.. .whereas, the Capri Sun is actually sweetened with Splenda...I figure the less additives the better:)
Also, this may work for your three year old (your 1 year old is probably still too young for this), but there is a website called handcharts.com. It is a website that has a chart that can record your childs accomplishments (some of those being drinking milk and water) and then there are games on the site, they have a cat that they can buy clothes for and dress up and they can earn points through good behavior (drinking water) and use those points to buy more clothes for their pet, or 5 minute cartoons. My kids love it and have been so much better about their milk AND water.
One other thought is what your kids see you do, they will do. Go to Walmart and buy all of you a cheap water bottle and always keep it handy for them to drink out of and if they see you doing the same they will do this too. I drink water all day and this has helped with my kids doing the same.
Sorry for the long response, hope this helps!!