I saw a macro today that read, "Just so we’re all clear, it is okay to miss people you no longer want in your life."
Useful advice, that.
The decision to cut ties with someone who is a close blood relative or someone who occupies an important emotional role in your life is never an easy one. Sometimes, removing someone important from your life seems about as appealing as cutting off your own arm or leg, but it has to be done to preserve your own mental or physical health.
But if your emotional attachment had any depth to it, out of life doesn't mean out of mind. You will miss the good things -- and there are usually going to be good things to remember, because humans are complex beings who are seldom complete monsters. Incomplete monsters can still make you a fabulous breakfast or take you to Paris. Sometimes, you will miss what you never had, but should have. You will think back and mourn opportunities lost. You will mourn the loss of love.