Does a Muslim sin for intensely disliking another Muslim if that dislike is confined to the heart, and is the sin of severing ties of kinship قطع الرحم absolved if one greets a disliked relative with the intention that this greeting is for that person?

The fundamental principle is that a Muslim should not harbor hatred towards any Muslim, except for the sake of Allah. A Muslim should allow the Sacred Law to govern their emotions, so they love a Muslim in proportion to the religiosity they possess, and they hate and dislike them in proportion to the transgression they exhibit. The severance of estrangement between Muslims is achieved by extending greetings (salām). Connecting with relatives is obligatory, and merely greeting them is not sufficient.