Rav Sternbuch (Teshuvos v' Hanhagos 2:449): Question: A son wants to move to Israel but this will be detrimental to his father and he will lose the mitzva of honoring his parents. Answer: The mitzva of settling Israel is a dispute among poskim. Even though it is clearly a mitzva to dwell in the holy land of Israel, nevertheless some say it is only when the person is able to experience the holiness and thus is elevated by the experience. However someone who is not assured of spiritual elevation but just wants to go to Israel to be free of the burden of golus - then going to Israel is not considered a mitzva according to this view. [see what I wrote in Teshuvos v' Hanhagos (1:900). However concerning the present case, we see in Kiddushin (31b) that living in Israel seems to be equal to the mitzva of honoring parents. In this case where the son is actively involved in honoring his father and wants to move to Israel - perhaps it is not correct because of the principle that one who is involved in doing a mitzva is exempt from doing another and thus it would be prohibited for him to leave his father. Furthermore in the present case where he already is involved in the mitzva of honoring his father he should continue doing it and therefore it would be prohibited for him to move to Israel and to stop the mitzva that he has already started.
However if he claims that in Israel he will be able to better raise his children in Torah then since there is nothing comparable to the mitzva of education children - then it would take precedence over honoring his parents. That is the Torah law because nothing is comparable to the education of children because their entire future is dependent upon it.
Therefore it is necessary to carefully investigate whether the parents truly need his help. In such a case it would be prohibited to leave them and stop the mitzva of honoring parents. It would be prohibited in such a case to stop the mitzva for the sake of living in Israel. However if he must settle in Israel for the sake of educating his children - then he should definitely move because the mitzva of educating his children takes precedence because there is nothing comparable to it. In particular here in South Africa where the Chareidi education for either boys or girls is not as good as what he can get in Israel in the religious communities. (Look at V'Yoel Moshe of the Satmar Rebbe where he says astounding things in the name of major poskim that one should not leave a mitzva in order to settle in Israel. That means not to make aliyah when it means nullifying even such mitzvos as providing hospitality to guests so surely not when it means nullifying honoring of parents.)
In contrast if the situation is that the parents are not dependent on him - but rather it is nicer for them that he live nearby but that they won't be overwhelmed if he leaves and they will quickly adapt to his absence - then he should move to Israel because of the superiority of education for his children compared to what South Africa has to offer. However this is only if he can find a proper community in Israel as well as a livelihood (See what I wrote in 1:900 on this topic). This is what I think the general rules are in this matter. In reality it is necessary for everyone who faces this decision to seek advice from gedolim and tzadikim and through their advice they will be successful.