Yes they are signs of food poisoning
in the family...typically after eating a particular food together when multiple people have similar symptoms; that is harbinger of food poisoning.
As a rule any kind of poisoning, even a suspicion of poisoning should be brought to medical attention as soon as possible, because poisonings if traeted in time can be reversible and any delay can result in cumulative damage and at times proves fatal.
So take both of them to a hospital at the earlist, if you expect unavoidable delay, then keep them rehydrated with ORS
or home remedy with liquids like cocnut water, rice water, soups, Buttermilk etc.
Rule of thumb is slightly over replace the lost amount and replace even when vomtting episodes are there.