Praise be to Allaah.

I’tikaaf is Sunnah and honouring one's parents is obligatory, and an obligatory duty cannot be waived for something that is Sunnah; the Sunnah cannot be regarded as equal to something that is obligatory, because the obligatory duty takes precedence over it. Allaah says in a hadeeth qudsi: “My slave does not draw close to me by means of anything that is dearer to Me than that which I have made obligatory upon him.” If your father tells you not to observe i’tikaaf and he says things that imply that you should not observe i'tikaaf because he needs you, then the way he sees things is correct, not the way you see things. Because you want to do i’tikaaf, so you think that these reasons are not acceptable, but your father thinks that they are acceptable. 

What we advise you is not to do i’tikaaf. Yes, if your father says to you not to do i'tikaaf and he does not mention any reason for that, you do not have to obey him in that case, because you are not obliged to obey him in something that will not harm him if you go against him, and when there is a benefit for you in that thing. End quote.   

Shaykh Muhammad ibn ‘Uthaymeen (may Allaah have mercy on him) 

Risaalah Ahkaam al-Siyaam wa’l-I’tikaaf (p. 31).