Yes wierzyć requires Dative BUT
'wierzyć w' ...requires Accustive, 'wierzę w twoją miłość(Acc') NOT 'wierzę w twojej miłości(Dat)'
No. You can trust your brother and it's not about anything he said. You just trust him. You "believe" something that someone said.
"Nie wierzy w swoją córkę"
Which also has the same double meaning as in English: she doesn't believe her daughter can succeed / she doesn't believe her daughter exists
So here shouldn't it be 'wierzy w'? Because "she doesn't believe her daughter" feels like it is missing something, such as '...can succeed'. It feels like it is missing the object if we use 'believe/wierzy' instead of 'believe in/wierzy w'
No, it shouldn't. It's like in English: "I don't believe you!" = "Nie wierzę ci!" -> I don't believe that what you are saying is true.