It's that parent's turn to have the child. The child does not feel good, and that parent doesn't have any compassion.

No, it isn't up to the child.

If it is the other parent's court ordered time, then you have to prepare the child for that visitation. However, you do not have to force the child to go with the other parent.

If the child is ill, then explain this to the other parent and offer to switch times.

You can and should perhaps make a offer to exchange times, if this is every other weekend, let them have the next two in a row or something.

If the two parents work together. ( and they should for the child) But it is the other parents time, how would you feel if it was reversed and they did not want you to have the child during your time