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So far I know the language:
你的愛 = your love
我的愛 = my love
Does this sentence 你心裡明白 我對你的愛 mean: In your heart understand me to your love or In your heart understand my love to you?
In 我对你的爱, it should be broke up into 我 [ (对你的) 爱 ].
So 你的爱 is not a sub phrase here.
对你的爱 means love for/to you.
The sentence can be tranlated as: In (your) heart you understand my love to you
For/to your love
for/to + your/my + noun
Required, but never shown