Minding GC for four days

If you want to do this you will need to have someone "check in" with you a few times a day if you feel anxious.

I wouldn't want to do it alone and I know I'd be too tired by day 2 or 3 to be any use.

Good luck if you do.

My husband was a fit and healthy 62 year old when he had a stroke, he was walking home after have had his eyes tested. Sudden illness can occur out of the blue anytime. Being anxious and probably tired can won't help the situation. I would say no unless you have some back up.

What you perhaps could do is ask a friend to come along with you. You could say it is because you lack the confidence to look after the children alone. Alternatively ask for contact details of any friends or neighbours that you could ring in case you need to. This might give you the reassurance you seek.

Far too much to ask, IMO.
I’d be worried, too, about ‘anything happening’ to me.

We’re having the Gdcs for 3 nights, 4 days over half term, but they’re 3 3/4, 7 and 8, relatively easy now. Dh will be here to help but TBH I will still be knackered at the end of it.
(We are 74 and 76.)

I was exhausted after looking after our 2 GCs when they were tiny and I had MrOops to help. On the 4th day he had to take the day off and I stayed in bed.
You need back up, what if you get Covid?

When in doubt, don’t.

I would be thrilled, I have no reason to expect any sudden fatal events in my life.
Seriously if you are young and fit enough to cope with them then don’t worry. If they trust you you are quite honoured.
It is not good for you to live your life anticipating imminent doom.

Many years ago a friend used to look after her baby grandson in her home, while her daughter was working.
One day the mother arrived at her mother's house to collect her baby.
Baby was safe in his play pen.
Grandma, aged only late 40's lay dead on the sofa. She was perfectly well earlier in the day.
So, no, you are not being unreasonable. It's too much responsibility without back up of some sort.

4 days and that young is a lot

If you do not feel comfortable, the parents should respect your decision and make other arrangements

My daughter and her husband leave my grandson for a night or two now and then, but they get my SiL's parents to come and look after the toddler in his own home. They have never asked me - I'm a widow and I think they realise I would be very anxious having sole charge. I think it's much easier if there are two pairs of adult hands available. So, with TWO children for FOUR days, I would just say it's too much for you by yourself. What about the DiL's family, can't they help?

Between one and three! Well I have been a very hands on gran but to have full responsibility on your own for 4 days (4 long days) is too much. Tell them it is too much. Would cause you too much worry. They are babies and no matter how caring you are they are not your full responsibility. Say no.

No I definitely wouldn’t do it, I think their far too young.As vegansrock said a lot can go wrong. I would tell them to put it off until the children were at school all day, much easier.

How far is your Son's house from your home? Do you have a friend who could stay with you and help.. or do they have close friends you could call on, or their babysitter maybe. I think it could be doable if you have enough help but it will be completely exhausting even with help..

I would decline, I love my grandchildren but would not do what you have been asked to do. I think it is a cheek of them to even ask you for that matter!

at their ages they will cry for mummy/daddy when awake in the night.

I understand the thoughts of the parents as they will not think about anything bad that could happen to you.

If that is your only concern then you could have someone contact you at various times during your time there to make sure you are okay. Do they have neighbours close by that would be aware if something had gone wrong?

It is not something I would want to do as I do not like having the responsibility of caring for young children. I would be in a state of anxiety for the whole time, it worries me when I have to dog sit for relatives.

1 and 3 for 4 days - a lot could go wrong! They will be missing their mum and dad, may wake through the night and will certainly be up at the crack of dawn. And want feeding and entertaining all day. I wouldn’t do this on my own to be honest.

Is there any reason to think you may become seriously ill over these 4 days. You don’t mention your age in your post.
If you would like to look after the children I am sure your son & dil have friends nearby that you could contact in an emergency or just to check in with you over the 4 days.

I think you are being sensible. The children are very young and the overseas break is nothing that can't be put off until the children are at least old enough to know what to do in an emergency.
That said, have you any other adult children who could join you?