Based on my experience with ropinirole changes in behaviour are subtle and can be hard for anyone to spot. Having said that if you have noticed an increase in time spent on internet gambling it probably is time to take action. I think that blocking the site is a good idea and something you should try very hard to stick to.
I was on dopamine agonists for 3 or 4 years and latterly I was out of control. I wasted huge amounts of time, but luckily not much money, on pointless web surfing. I have cut out dopamine agonists altogether now but I still try to stick to a rule that my laptop never goes into my bedroom.
It is worth talking to your neuro/nurse/gp about how you are feeling. As ever the advice is not to vary your dose of meds without professional support. In particular stopping suddenly is dangerous.