Why did Sarah demand that Hagar be expelled together with Yishmael?
Rashi (in Mishlai, 29:15): 'Yishmael's wickedness caused Sarah to demnded that Avraham expel Hagar and him'.
Seforno: Refer to 21:9:1:1.
Ramban: Because the young Yishmael would not have managed to survive without his mother.
What made Sarah declare with certainty that Yishmael would not inherit Avraham?
Seforno: Because he was the son of a slave, and if one of the parents is Pasul, the child's lineage is that of the Pasul parent 1 - rendering him a slave, who is not considered an heir.
See the Mishnah in Kidushin 3:12.
Why did Sarah state both "Im B'ni" and "Im Yitzchak"?
Rashi: What she meant is that Yishmael would not be worthy to inherit Yitzchak, even if he (Yitzchak) would only have been her son but not as worthy as Yitzchak, or even if he would have been as worthy as Yitzchak but not her son, and how much more so now that he was both her son and Yitzchak!
Targum Yonasan: Expel Yishmael, Sarah was telling Avraham, a. because he is not fit to inherit with Yitzchak and b. so that he should not wage war with him over the inheritance.