Summer holiday and mil

Could you say ‘maybe next year’ and then in the coming year have her stay at yours and you leave her with the children for a night or two to see how it goes? You could be not too far away and the children would be in a familiar environment? ( ideally without the Akita)

4 is too young if they haven’t been away from you for more than 1 night. It sounds like an amazing opportunity for the 9 year old to bond with their DGM and have an adventure though. Lots of schools have residential trips at that age. TBH there are only a few years left when your 9 year old would want a holiday with granny. They will have better things to do once they hit their teens. It would be a shame if they missed out on that childhood experience.

Maybe just the 9 year old could go? Or, as you suggested, have a trial run nearer home first.

I think 4 is a bit young. I agree, you want to try some nights away but where it's easier to get them if it doesn't work out before considering something like this.

If you can't stay with her, why don't you all go away somewhere new as a family?

Why doesn’t she come and stay at yours for a few days, and you can have a couple of nights in a nearby hotel? The kids would be in their own home which might be easier for the first time, and she can spend quality time with them / have a taste of what 4 and 9 full-time for a few days is like!

I'd say no.. I think your suggestion of her taking them somewhere closer is a great idea

Happy memories of staying with my grandmother with my sibling. We were 9 and 12. 4 is far far too young to be separated for days and so far away from you

I travel a lot and have yet to come across somewhere where accommodation is exclusively that expensive. Maybe you could put the dog in kennels to make it easier?

I wouldn’t send the kids alone if I wasn’t happy with it but I would make arrangements so my family could visit MIL

I wouldn't agree to this, no. But I do think it's reasonable to try to find a compromise or to work towards MIL being able to take her GC away if she wants to. For example, if she's never had them overnight before you could suggest you all go away together for 1 or 2 nights somewhere, so that MIL gets used to the kids bedtime routine etc. Then you might feel more confident that they would settle for her if she were to take them away in future, somewhere closer to home like you've suggested so that you could get there in an hour or two if needed.

Rather obviously no. Would she go on a break with you all somewhere? I would not leave the dc that far away at that age, particularly when they haven’t done it before.

Is it something the 9 year old would be up for doing alone? For that age it would be a maybe for me, but 4 is deffo too young in my book.

Also, if she’s pushing back and getting insistent/grumpy about it, that’s a pretty good sign the dynamics aren’t right for it just now!

Could you offer to have her visit more or meet up somewhere more affordable on the mainland, with the express idea of building up to this in the future?

It's a NO from me

Say no. That won’t work well

Assuming she is capable of sensible decisions I'd let them go for it

Like bringing strange kids into a home with an Akita? After an absurd journey requiring the whole family to make a several-hours-long journey just for the parents to return home, to do the same thing in reverse a few days later, just so she can look after dc in her own home?

I'm not reading sensible in any of this op. Hard no from me.

I completely disagree with you @TheBigFactHunt

I think either the MIL takes the children to stay somewhere nearish to where the OP lives or that the OP stays somewhere nearish to where the MIL and children are staying are both much better options.

This would be a hard no from me. I wouldn’t even entertain the idea. ‘Thanks for the offer MiL but that arrangement isn’t right for us at all at this point.’

Really? Where does she live?!

Assuming she is capable of sensible decisions I'd let them go for it. What a great adventure for the children, and spending time with their Grandmother is priceless. If she was to become incapacitated or worse, you'd regret not allowing them this opportunity.
Whenever I feel particularly worried about children doing things without me to be the emergency backup I am reminded of Finding Nemo.
Perhaps you and your partner could plan a few nights away near the drop-off point?

Staying with a strange dog, somewhere that involves a three hour ferry ride. .... no. You can hardly go and fetch them if there is a problem.

It would be a no from me.

The DCs may enjoy seeing her when she visits but I doubt it's often enough for them to know her well enough to be a long way from home with her.

It's too far and takes too long for you to get there if you had to. What's DH's take on this?

“Maybe when they’re older. “
Could you and DH use it as a break, and stay somewhere not too far away yourselves?
How would MiL be anticipating the travel arrangements? If she’s thinking you’d be doing the transportation, is she prepared to cover the cost of it?