I said the OP has the right to request a termination of the holiday and support if she feels she cannot cope. It does not seem that the child is seriously ill such that the hospital believes the child needs to stay in hospital, so one half of the couple terminating their holiday doesn't necessarily need to happen, or have to be a cause of contention provided the sitting partner can cope. My view on what I would do is relevant when the OP is asking for a range of opinions. Of course she'll do what is best for her.
What I disagree with (in the absence of further context not given, for e.g. is the man generally fickle in other situations, unfaithful, immature etc) is the assumption that one part of a couple still going on holiday necessarily equates to that partner not giving a damn about their child, who is, by the OP's own admission, typically illness prone, but not seriously so. To frame it that way is destructive immediately. When in reality some people would be able to say, 'no love, I don't want you to not go on your holiday. You go and I hold down the fort.' That is perfectly legitimate within, as I said, a context of a usually good secure relationship.
It can be negotiated and shouldn't be boiled down to a caring olympics.
If the child were seriously ill, that would be a different matter, but in light of the information provided it doesn't seem that serious. So what I read is this is an insecurely attached relationship, where the OP already doubts her partners commitment to her and their family and this is therefore further proof of that, whereas if it were a mature relationship where the partner was usually supportive, the possibility of him still going on the holiday would be there as an option to negotiate and not necessarily perceived as negatively as it appears to be here.
I definitely don't approve of the family adding fire to flames at this moment in time.