When Palpatine first tells Vader that Padme is dead he screams. It is a scream of pain, despair, denial, and other emotions that he can't place. (Couldn't have placed at the time and didn't go back to try later.) They sedate him after he destroys most of the medical center.
Later, he tries to figure out how he feels. He walked into Hell itself, willingly, knowingly, to prove himself worthy of her love. But when he sees Naboo burn, he is glad she is dead. He sees a girl, a child really, run to try and hide behind a statue. A stormtrooper shoots her and as her body falls he recognizes one of her nieces, but looks away so he won't find out which. That's when he notices the statue is of Amidala and she now looks to be crying tears of blood. And he is glad she is not there. He is glad as he walks though Theed's ruined streets past rubble and bodies and gutted remains of beauty. As he lays a perfect rose on her grave, the only thing untouched, he rejoices.
He loves her so he is glad she is not in pain.
When he sees summer rain he is miserable she is dead. She used to run out into the field and dance in the rain, loving it and looking so alive that he nearly dies of anguish remembering and tries to block out the half-felt ghostly raindrops on his skin. He remembers the laughter on her face as she reached out a hand for him to join her, the rain making her hair stick to her head and her clothes to her body. He remembers the falling drops running down her face making her look as if she were crying, but only tears of joy. And he almost does a very un-Sith-like thing underneath his mask and almost has tears in his eyes. But if he cried, which he won't because he's Darth Vader and Dark Lords don't do things like that, they would not be tears of joy.
He loves her so he is miserable she is not happy.
When he kills the remainder of the delegation of 2,000 he is pleased she is dead. He is pleased and he takes care to kill first the women there who look most like her so they cannot witness his next actions with her eyes. But even after her death Sabe sits and stares and watches him with blood trickling out of her mouth making it look like the scar of remembrance she wore as Amidala. So he pushes her body away with the Force and now does not have to feel brown eyes on his back, judging him and finding him guilty. Then he turns on the others, recognizing some of her old friends and allies among them and smiles even though no one can see. And if they could they would probably think it was because he was cruel or vindictive. But he is merely pleased. Pleased that she cannot hear their screams. Pleased that she doesn't know how some remained defiant and how some begged for mercy but he didn't care either way.
He loves her so he is pleased she cannot condemn him.
When he refuses to discriminate among his soldiers, uncaring of wealth and "status", he is sad she is dead. Sad that she is not there to praise and support him. Sad that she cannot light up his whole world with one of her smiles as she not only approves, but helps. He knows she would, the handmaiden queen who smiled at a slave and who finally loved and married him. Further more she would be able to help more so than before. She would be the queen of the known galaxy, the empress. He was not and would never be a politician and would let her rule the universe as she ruled his heart, as her unquestioned right. She would be kinder than Sidious and he wonders, briefly, if the good of the universe might have swayed her all those years ago. His love clearly did not have great worth in her eyes. But the rest of the universe… but then his mind goes off into a trail of "if only" that he has traveled far too many times as he remembers when she called him a hero.
He loves her so he is sad she cannot encourage him.
But as time goes on he has more and more times when he is relieved that she is gone. He causes death and she is not there to mourn. He enslaves and she is not there to save. He invades and she is not there to fight. He tortures and she is not there to condemn. He enters the cell of the young princess with a face far too much like Padme's and a tongue far too much like Anakin's and she is not there to hate. As he leaves he feels a mixture of guilt that brown eyes like Amidala's were full of pain because of him and relief that they weren't her eyes, not this time. And he clings on to the relief to get rid of that notion that crept out of nowhere that she would hate him for this act more than anything else he's done until then though he doesn't know why and further more doesn't want to know why. For he has undergone many things in life but knows he would never survive her hatred. If she is not alive, than he can love and mourn her without worrying what she would think, what she would say, what she would do. If she is not alive she cannot hurt him for only those you love can ever truly hurt you and the emperor's lightening is nothing really, a hutt's slave is not treated well and he is very used to physical pain.
He loves her so he is grateful that she cannot hate him.
When he learns of Luke he is in despair because he realizes a part of her has been alive all along.
And Luke hates him.