Make that another suggestion for either bringing a laptop/ Cell type device to the parks, or a smartphone which will allow you to do your work.
Depending on the type of work you need to get done, the Business center option may not meet your needs. If you are needing VPN access, it's pretty certain that you would not be able to do that at a hotel's business center, and even if you found an open WiFi connection, there is no guarentee that the WiFi would support VPN tunnels.
From a Vacation Enjoyment standpoint, the Laptop/Cell (or Mifi) solution would allow you to stay in the parks with your family, Even if it means you need to skip a ride or two, It's much easier (and less stressful to the entire group) for you to plant yourself at a bench while the family watches a performance or rides a ride. Depending on your time requirements, You could even grab a bite to eat or snack and grab a table someplace to do your work.
a locker for the laptop would allow you to have it within the park and not have to tote it around if you didn't want too.