When our children were young DH and I had weekends away without the other, but each of us managed perfectly well on our own without any need to call in anybody else to help us manage, including when the children were ill.
DH's job took him away from home frequently for indefinite periods of time, on one occasion for over six weeks. If I had been unable to manage, DP and DPiL would have to moved in to cope with all the absences.
Personally I would have felt quite insulted if anyone had suggested that I might not be capable of looking after DC on my own and might need extra help.
NanKate if your children cannot cope with looking after the children on their own they should make sure they never put themselves in that position. Tell them to cope on their own. They will soon learn.