Rather late in the day, but I can't see what the issue is. She's off sick from work. That doesn't mean she can't turn up at the work place. I see absolutely NO issue at all.

In addition to David's point, it really depends on the circumstances.

What is the work event and what is the nature of the illness? The work event sounds like it involves children at the school so I'm guessing it is more of a social rather than training or reward for staff. E.g. a summer fair, sports day, summer play etc.? If it is social, rather than work, there's no reason they can't attend especially as a parent. If they are looking to take an active role, such as staffing a stall or manning the front desk, I'd be clear about whether they're intending to do so in their capacity as staff or as a parent - as it's quite common for parents to volunteer at events so it doesn't necessarily link to pay but it's good for everyone to be clear before it happens.

What is the nature of the illness? If it's contagious, it's reasonable to ask them to stay away. If it's a physical ailment, it's reasonable that they may be able to support an isolated event but not do their usual role - equally it may also pose a risk, depending on the nature. If it's a mental health challenge, it may be helpful for them to find an informal way to interact with colleagues and students. On the other hand, if they're saying in absence reviews that they can't possibly attend the work premises because it is too triggering for anxiety or trauma...you might have some questions at the next absence review about how their experience of this event was and what made it manageable, what elements of that can you recreate for them to be able to come back to work etc.

Is it inappropriate? In some, very select circumstances. Should you approve? Almost always yes - and do you need to approve? Do you approve other parents attending without their children?

In reply to Sophie:

Depending on the reason I would risk assess this, my example would be an employee who has just been signed off after a medical procedure and was still recovering. Our view point was their safety or others compromised?