Clearly, the main example of parental love vs. parental control in this play is going to concern the relationship between Brabantio and Desdemona, his daughter who secretly marries Othello behind his back. You will therefore want to focus upon Act I scenes 1, 2 and 3, where Iago hatches his plan to create problems for Othello with his new father-in-law. Consider Brabantio's rather distracted response to realising that his daughter is not in his house:
It is too true an evil, gone she is,
And what's to come of my despised time
Is nought but bitterness...
O unhappy girl! --
With the Moor, say'st thou? - Who would be a father?
We can see the tension between parental love and parental control here given Brabantio's sadness for both himself and his daughter. This is something that continues to be demonstrated in Act I scene 2, when Brabantio enters, accusing Othello of having "enchanted" Desdemona and of being a "foul thief." In Act I scene 3, he protests to the Duke that his daughter is considered "dead" to him:
She is abused, stolen from me and corrupted
By spells and medicines bought of mountebanks,
For nature so preposterously to err
Being not deficient, blind, or lame of sense,
Sans witchcraft could not.
Clearly the strong words regarding how Brabantio believes his daughter is "dead" because of her elopement continues this tension between parental love and control.