How do I fix a Lixit valve bottle?

I have had this Lixit valve bottle - the blue flip top one - sitting around for months because water does not come out of it. Today I decided to take the valve apart to see if there is some mechanism I can loosen to let the water flow when the valve is pushed. Um. I can't find a way to get it apart. Does it not come apart? Does anyone know? If it doesn't come apart, I don't know how I would clean out the valve either, which I'm sure is important to do occasionally.

Right now Elena is on a glass water bottle with the ball valve, not sure of the ounces but it's big for one chin. When I had Tseng too it was fine, but now she just doesn't drink enough of it before I have to clean it so I have to dump most of the water if I want to clean it daily or even every other day. I'm not using tap water so this is a huge waste of water I'm paying money for. So I got a smaller bottle. The thing is, it has a smaller valve, and a smaller cap, and she wouldn't use it. I don't think she was getting enough water out of it. And the bigger ball valve cap doesn't fit on the small bottle. So I got the Lixit, hoping she would be ok with the push valve, and I can't get it to work. Frustrated!

So is there a way to adjust the flow on this water bottle or is it just a lost cause? I really don't want to toss it if I can fix it, but if there's nothing I can do ... and it's way too late to return it. Does anyone know about the secret inner workings of the Lixit flip top?

Thanks,
Danielle