I’m taking my family swimming at Beau Sejour / going to the cinema / doing something that costs to go to……. Am I expected to pay for the student as well?

Yes, if you have decided to take your family on such an outing then as you would pay for your own children then it is expected that you would pay for your student too.
However, if you are going to an event such as the West Show or a Seafront Sunday for example, then students should take some of their own money to cover for any of the attractions or desired purchases once they are there.