I have recently purchased PSE11 and have installed it on my home desktop computer and my laptop
My daughter would like to use it occasionally on her laptop. Providing only one computer at any one time is accessing the application would this breach the EULA or prevent the application from working?
Yes, you are only allowed two activated copies at any one time. You would need to deactivate it on one of the other computers to install it on the laptop, or purchase another copy.
I think that there is a limited number of activations/deactivations. Is that true?
Yes, but it's a fairly large number.