Like was said above, you need a water-resistant emulsion. Most have SOME resistancy, but there are ones specially made for water-based inks. Ulano TZ and Ulano 925WR are made for water based inks.
I got really confused by your explanations so I'm just going off what I think you're saying.
If you underexpose the screen, and then print ink into it...you've just meshed ink with emulsion and it's probably not going to come out easily, if at all. When the emulsion is over exposed, it can just be too "locked in" and require much harsher chemicals (haze removers) to remove them.
Waterbased ink evaporates when it sits in the screen for too long. It's best to keep a spray bottle of water nearby and a can of waterbased screen opener close at hand to keep the screen from clogging up. Once you are done printing for a certain amount of time (I clean up after 10 minutes) scrape all the excess ink off the screen and put it back into the container, cap the container and then spray the screen with the screen opener. If you're only going to be gone for a minute or two, spray a few sprays of water into the ink to keep it moist.
Usually when waterbased inks completely dry inside the screen, it hardens to the emulsion which makes it extremely difficult to remove. The haze removers I mentioned above might not even be able to break it down, and are hazmat products that should only be used in the proper washout sinks with recirculating tanks as to not put it down the drain.
You should check with the manufacturer of emulsion you use to see if they have a more water resistant emulsion than what you're using. I know Ulano has a few standard emulsions that you can add a Diazo to that will increase water resistancy. You can also use a Hardener as mentioned already or re-expose the screen too.
I also recommend finding proper exposure times based on the emulsion you are using and the exposure unit you have. The best emulsion in the world won't work if it isn't exposed right.