How does Shakespeare portray Portia's relationship with her father in Act1:2 of The Merchant of Venice?
It is in Act I scene 2 that we are told about the caskets and how Portia's husband will be selected because of a riddle and test created by her father to ensure that she marries wisely. Of course, Portia, being an independent individual, is none too happy about this test. Consider how she describes it:
O, me, the word "choose"! I may neither choose who I would nor refuse who I dislike; so is the will of a living daughter curbed by the will of a dead father. Is it not hard, Nerissa, that I cannot choose one nor refuse none?
It is evident from this description that what Portia craves is the ability to make her own choices and select her own husband, rather than have her husband selected for her by a kind of lottery created by her father. If you are looking at conflict, this is a massive conflict that Portia needs to endure - the will on the one hand to select her own husband, and on the other hand to wait passively until a suitor selects the right casket.
But consider how Nerissa responds to Portia's complaint:
Your father was ever virtuous, and holy men at their death have good inspirations; therefore the lottery that he hat devised in these three chests of gold, silver, and lead, whereof who chooses his meaning chooses you, will no doubt never be chosen by any rightly but one who you shall rightly love.
Nerissa assures Portia of the wisdom of her father and his good judgement in designing this lottery. Portia just has to accept that the wishes of her dead father will overpower her own desires for independence. You might find it interesting to examine how the character of Portia develops and how she becomes a subservient wife by the end of the play - in contrast to the feisty Portia that saves her husband's best friend from a difficult spot.
I totally agree with just about everything accessteacher said. However, I don't agree that in the end Portia is subservient. When she gives Bassanio the ring in Act III, scene 2, she gives him everything including herself but says, "...I give them with this ring,/Which when you part from, lose, or give away,/Let it presage the ruin of our love,/And be my vantage to exclaim on you." For Portia, the ring she gives him is a symbol of their love but she also warns him not to take it all lightly.
Bassanio does indeed give away her ring and by doing so tells her that his love for his friend is higher than the love he has for his wife. She calls him out on this in Act V. It is a warning to him and she gives him a second chance but Bassanio knows that she is a no nonsense type of woman. Perhaps it is at this moment when Antonio does not come to his aid, that Bassanio realizes where his love truly lies.
As for her relationship with her father, I would like to add, that it would appear that her father knew her well. I like to think of Portia as an iron fist in a velvet glove. He also knows the world in which she lived and was protecting her against fortune hunters. The caskets and the strings tied to them were a great protection. It would appear that Bassanio loves her and not her fortune because he does not go for the obvious. Of course, Portia's gentle hints help but he does choose correctly.
At the end of the play, Portia has taught her husband the true meaning of love and how a marriage is a partnership. This is true of most of the comedies. The women teach the men.