Two questions:

 

1. Can I bring in a water bottle to refill with water or do I have to buy their souvenir cup?

2. Hitting the regular park and water park in same day. Do I need to bring in a towel? If so, is there somewhere I can store it while were not doin the water park?

question 1  yes you can I put mine in my cargo pocket and have never had a problem  I don't do water park so no answer for # 2

Yes, you will need your own towel for the water park. You could put it in a locker or if you don't feel like spending money on that you could also easily run it back out to your car.

Just to add, small (7oz) cups of water are available free at most food/drink locations. Just walk up and ask for one.

I have a couple of 16oz collapsible water bottles with sport caps.  Essentially a Mylar bag with a small carabiner I use for additional water between stops.  Much easier to take on rides.  

We do both parks in one day frequently.  I usually stuff towels and a change of clothes in a basic backpack and keep it under my chair at the water park.  Change in the showehouse then go to the car put on shoes and drive over by the dry park enterance.   

I rarely get a locker at the waterpark and only when I need to have my phone more available for some reason.   Otherwise I am not really concerned about loosing some sunscreen and a few towels and I have never had a problem though it could happen.  

Personally I need to take a shower after the waterpark especially if I go in the wavepool.   The water is just sticky from all the sunscreen, don't know why I don't have that issue from the slides or river.  

I do not bring a towel in and generally just air dry.  I usually walk out to my car and change (we have blacked out windows) so I dont have to carry any thing of value inside the park.  It can and will be stolen!!!!!  

I also bring in my yeti cup with out any problems.