I remember being pretty exhausted a lot of the time in my mid-20s with two children aged 1 and 3, let alone doing it now for 4 days! It sounds too much to me, particularly on your own. I'd have to say no in your situation unless there is someone, a close friend, who would be willing and able to share the responsibility with you and that the parents would trust to help you.
It's always been one of the downsides of parenthood for most couples that compromises have to be made, and trips away without the children are one of those compromises in this case, I feel.
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