Hi J.,
Rest assured that even in scientific experiements, scientists monitor hydration levels by urniary output - so if she does have a good amount of urine in her diapers then you know she is doing fine. If your changing her diapers every 3-4 hours and they are not really heavy, then she probably needs something to drink. Also, if her stools are hard or pellet-like then thats a sign that she's either held it in a long time OR she's dehydrated and her body has reabsorbed the water from her stool (if she holds it in a long time this will happen regardless of how hydrated she is).
That being said, it seems like she's asserting her independence through this. If it were my daughter, I would combat that by making a sippy cup around her all the time - that way she can drink if she feels like it even if the moment only lasts for a second. Fighting also looses it's appeal that way. For us, the boys have a sippy cup near their play area from the moment they get home until bedtime; in the morning when they wake up and with meals, and whenever we go anywhere.
If she's in a daycare setting at all, I would express your concerns with the provider and see if they can help by providing drinks more often. I bet they would be happy to help.
Another thing you can do if you're still concerned, is adding liquid to her foods. As a mother of 17 month twin boys, I know how messy that is, but it'll get fluids into her. Give her soups, oatmeal with breakfast, scrambled eggs with some milk mixed in (before cooking), maybe even using jars of baby food like the mashed green beans, bananas, pears, or whatever she likes, because those have water in them also. We still feed our boys soup on cold days even though it takes forever, use Stage 2 or 3 baby food if it seems like they aren't consuming enough fruits or vegetables on their own. We do it for nutrition and variety despite the insane amount of mess it creates, but it can also be done for hydration. Also, fruits and vegetables have a large percentage of water in their weight, so if she eats those food groups well, she's getting more fluids in than you'd think.
Good luck! Hope some of this helps!