A stepmother home alone with her step son of 16 and step daughter of 12
If the son and daughter are siblings it surely isn’t a problem. If they are not then it is controversial. R’ Moshe Feinstein ruled that yichud is permitted, but only if the stepmother is married.
Even according to the other poskim who say that it is yichud, this issue can be avoided by giving a key to a neighbor or to relatives and asking them to come in, in order hat it shouldn’t be yichud. This question should really be discussed in person with a competent rov.
Igros Moshe E”H 1- 64,2, Nitei Gavriel Ychud 4- 6,7, Dvar Halacha siman 3- 3.