Translation:I also once thought I did not love your father.
Germandy is correct that ‘Ich dachte auch einmal, ich würde deinen Vater nicht lieben.’ can have both meanings: the conditional one (“I also once thought I would not love your father.”) suggested by Soglio, and the apparently past-tense one (“I also once thought I did not love your father.”) given by Duolingo. However, the latter is not actually past tense; it's subjunctive, because it's counterfactual.
The catch is that the subjunctive form of ‘werden’ is identical to the present-tense form for ‘ich’: ‘ich werde’. In such cases, the conditional form (‘würde’, in this case) is usually substituted.
Thank you for your help. For my sins, I must wrestle with the subjunctive past perfect, but with help, I may yet learn it. ;-)
If I'm not mistaken, both can be correct, but have a difference in meaning. I'll try to explain by changing the sentences:
I thought I did not love your father, but in reality I did.
I thought I would not love your father, but now I do.
The "would" refers to something in the future, like "I thought I was not going to".