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 for a short time, 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 4- 64,2, Nitei Gavriel Ychud 4- 6,7, Dvar Halacha siman 3- 3.