How can I argue that Emily's life has been negatively affected by her search for love and that Emily's (overprotective) father is at the root of her problems?

Emily is very much the product of a strict, loveless upbringing. Her stern father turned away every suitor who showed any kind of interest in his daughter. More than anything, this had the effect of keeping Emily in a state of arrested development, preventing her from growing into an emotionally-mature adult.
Deprived of emotional support for so many years, it's not surprising that Emily came to develop a somewhat warped view of love. For her, love has come to mean possession and control: the kind exerted over her by her father. Just as he wouldn't allow Emily to grow and develop as an adult, so too will Emily not allow the unfortunate Homer Barron to lead any kind of independent life away from her.

Emily Grierson grew up in a home with an overprotective, strict father, who stifled her social development by continually rejecting each one of Emily's male suitors because he thought they were never quite good enough for her. Emily's relationship with her father is best illustrated by the tableau, which depicts Emily's father standing in the foreground holding a horse whip while his daughter timidly stands in the background. Under her father's constant supervision, Emily lived an oppressed life, which dramatically impacted how she viewed love and relationships.
Emily's father's authoritative nature had such an effect on her that she even refused to acknowledge his death for several days after he passed away. One could argue that Emily's father's harsh nature led Emily to believe that love was associated with suffering and oppression, which is one reason she decided to poison Homer Barron and sleep next to his corpse for numerous years after his death. Essentially, Emily inherited her sick and twisted perception of love from her oppressive, authoritative father, who drastically stifled her social development.