With some difficulty unless you have a car. Don't even think about getting a bus. Takes 3 hours or more and I think only goes once a week. Are you going with a tour operator? They may offer it as an excursion, but more likely would go to the waterparks in the south such as Western Park in Magalluf. Otherwise, maybe there is an independent excursions operator down around Cala D'Or but I don't know of one.

My advice would be , don't bother . It is quite expensive to get in and very small compared to the parks at either Magaluf or Arenal . Your kids would be bored after an hour or two . We drove to the Aquacity park in Magaluf from Alcudia last year in under an hour and had a fantastic day.
It was also cheaper to get into than the Alcudia park.

I agree with the others,
You can get to Aqua city by Arenal in less than an hour where there are loads of activities for kids of this age.
The Magaluf parks would take 1 hour 30 mins to get to.
Trips by coach are on sale all around Cala Egos with your ticket for the water park included in the price.
The coach leaves at 9am and returns at 6pm daily in September from places around Egos and Cala D'or.
We found Alcudia park more suited to very young kids with just a few slides for the older kids.
Steve.

Thanks for all your replies we really appreciate the helpful information.

As others have said, forget Hydropark and go to Aqua City instead. It's loads better.