During a recent Pirkei Avot shi'ur in my synagogue, our rabbi discussed two concepts.
Jewish Virtual Library citing of Talmud, Tractate Kiddushin 31B
Our Rabbis taught: What is "revere" and what is "honor?" "Revere" means that the son must neither stand in his father's place nor sit in his place, nor contradict his words nor [even] support his words [when he is arguing with another sage]. "Honor" means that he must give him food and drink, clothe and cover him, lead him in and out.
Pirkei Avot chapter 5 (I think Mishnah 18? need to edit, later) states a person's lifetime "milestones" by stating that at age 18 one gets married, and at 20 he seeks work.
The rabbi made a conclusion from these 2 citings. He stated that according to the Talmud's teachings, a parent is obligated to support the children until age 20, after which the child is expected to be financially independent. Yes, he acknowledged that, among current Jewish religious society, there are numerous parents supporting their kids in yeshiva, Kolel, etc. but he pointed out that according to the Talmud, it seems that this is not the recommended method.
However, the 1st citing from Kiddushin seems to make clear that children are continuously obligated to financially support the parents, at least to the point where they must make sure that their parents are fed and clothed. This obligation never ends as long as the parents live.
If the child has only enough money to feed or clothe his own children or his parent, but not both, who gets the priority - the parent or his own children? Does it matter if his children are below or above age 20, per the above assumption? Are there any other criteria that would favor one priority over another, that I haven't mentioned?