Would you resent me if I was your employee or colleague ?

Have you actually been explicitly told your colleague will have to cancel their holiday?

I would be shocked if there wasn't a contingency plan - the likelihood of two people being unavailable to work at the same time is too high. And that's your employer's responsibility entirely.

Even if your employer had told you your colleague would have to cancel their holiday, I'd be suspicious. Cancelling an employee's pre-booked annual leave has not been a thing anywhere I've worked. They could be trying to guilt you into not taking paid sick leave because it's easier for them than trying to find a contingency plan. Again though that is management's responsibility, not yours or your colleague's.

Take the time off OP. If I was your colleague I would still be taking my holiday, if they have booked to go away, even more so if abroad. I wouldn't be cancelling it if I was them. Not their problem if work doesn't have enough people

Except she's not personally sick, her DC is. She even said she could 'work by the bedside', so definitely not 'too sick' to work. She's just not coping with her DC being poorly so should, quite rightly, take time off. But let's be honest about things.

Based on what you said no I would not resent you. I resent the colleague who in the past 5 years has had approx half of the time on sick leave coming back then using their AL 'learning the ropes' again before taking another stint off. I resent that person as their employer can't go through bloody due process to show they need to be fired and give us the opportunity to get a colleague that actually works more days than not and make work an ok place to be again.

Also look into carers allowance.

I hope your child and family are OK. Stay strong.

I'm an employer and I would say talk to your manager, even if parental leave is unpaid.

From a business perspective what is in a contract and what can be agreed on a case by case basis is often different. Its obvious that you can't work, and obvious that you could ask your doctor to sign you off, so your employer knows full well you will be off and you will need to be paid.

So if they basically know they will need to find a way to work around that and will need to pay you they may offer paid leave or find some other way to make things work,

But as an employer, I would be really annoyed if it felt like a staff member was gaming the system. Even (perhaps especially) if they had been with me for 10 years.

Just an honest conversation saying "I am so stressed, I need to be at the hospital, I can't work while I do it, but I can't afford not to work and my mental health is suffering" could trigger them to arrange something for you that also works out better for them as it might mean you agree to, for example, a regular catch up where you will answer any questions that are confusing whoever is covering your work, which isn't possible at all if you sign off sick.

If they say no, then go to the doctor and get signed off, obviously. But that's fine because you have told them you're stressed and offered them a chance to come up with a solution which works for you.

You need to be in sick leave

in terms of the colleague’s holiday its your company’s fault not yours. Have they actually said (s)he will have to cancel their holiday? If your role is so critical it’s ridiculous that another person hasn’t been trained up to do it even as an interim measure. Only two people able to do a critical task is nuts. Thats not your fault and your colleague should see it that way.

And I can believe how little empathy some people have...

Cannot you see that a parent with a kid in hospital is going to be massively stressed and not concentrating at work, sick with worry, not eating and sleeping properly?

This

Your child comes first and so does your own health - if you need to be signed off to maintain your own health then do so. You are no use to your child or your employer if you crack under the strain. Your employer is responsible for arranging cover, it's is not for you to worry about. Concentrate on looking after yourself and your child.

This. I have worked with many dedicated, hard working, senior people who made many sacrifices for their employers. 3 of those colleagues dropped down dead suddenly, many more retired after working decades of unpaid overtime. It is amazing how fast things just carry on as before. Put yourself and your child first. Nobody else will.

There are lots of people who take the piss at work. Yours is not such a case. Your colleagues would have no hesitation in going off sick if they had a child in need.

Do it, and don’t worry about work. If the shoe was on the other foot, you’d do it for them.

You have to put family and self first here OP, or you will break and not be back to work. Your manager and your colleagues would do whatever they needed to as well. Any resentment we would feel is ours to deal with and not your responsibility.
Your responsibility is
To care for your sick child
To maintain your mental and physical health
To assess whether you are capable to effectively carry out your work duties at the moment
Go see your GP and talk it over.

Definitely get signed off and try not to worry about what's happening at work as that is the managers' responsibility (I know it's hard not to worry about that). Prioritising your child and your health is very important. Sending all best wishes

I am sorry that your child is poorly and you are finding things difficult.
Do you have a partner? The other parent of the child? Could they not share the hospital time which could then mean your colleague could take their long planned holiday?
I do understand why you would want a parent to accompany your child in hospital but does it have to be you?

I can’t see anyone being annoyed with a single parent having to take leave and look after their child!!

Your work sounds shit. Cancelling a colleagues annual leave because another is unwell is not appropriate and the colleague should kick up a fuss and force them to sort alternate cover. This is a management problem not a you problem or your colleagues problem. You would not be unreasonable to take sick leave when you clearly are not coping and have become unwell.

Could caring be shared with DC's other parent or family step in occasionally to help?

Get signed off and be with your DC definitely.
However, I'm not sure why your colleague should effectively be penalised for your absence. You're two separate people; just because your plans change doesn't mean theirs should. I would not be cancelling a booked holiday because of someone else's situation. Your manager needs to arrange cover.

Is anyone else able to help with your child's care?

Take the leave and focus on yourself and your family.

Sending your child my best wishes x

Your colleagues holiday is not your problem - your employer sorts that out. I can’t imagine such a terrible situation, get signed off your in no state to work.
Your employment contract and benefits are nothing to do with anyone else they are between you and your employer. It sounds like you’ve been a brilliant employee so take the benefits.
good luck x

Op...get signed off and concentrate on your child and yourself. Caring for someone is exhausting and I can't imagine how you feeling if it's your child in this situation. Your colleagues will understand. If they don't that's more about them. That's what management is for to manage situations. Sending you hugs and strength Xxx

It’s not always that simple when your child is seriously ill in hospital either.

When my colleague's young daughter was diagnosed with leukemia she immediately went off sick with stress, our only concern was the wellbeing of her, her daughter and her family, everyone went out of their way to cover her workload without a second thought (and this was not a team normally known for it's compassion to other team members!). Please prioritise yourself and your child and get signed off x

Take the sick leave.

Your colleagues may be annoyed but ultimately, they will be grateful they're not in your situation and it's management's issue to sort out cover and holiday cover.

Look after you as your child needs you, not your colleagues!!