Like Hannah Anafeloz, Vincent could've stored his wife's soul inside him, so she could also see how her child was growing up. (In a way, it explains how girly his true form is which consists of high heels and dress-like cloak)
In the first episode, Sebastian entered the living room and the image of the Phantomhive family appeared. I don't think Sebastian spied on on a family if he hasn't made a contract with, and butlers are mostly by their master, but since Sebastian wasn't there at all, it means that he didn't make a contract. The only other option is that he was there, witnessing the moment. If he was Vincent, it could've just been him remembering the past.
It would also make sense that he wanted to protect his only child from the danger that the Queen's Guard Dog placement was. If Ciel had died in the fire or when they branded him, the Phantomhive name would exist no more.
At the same time though, he wants Ciel to know what to do in whatever situation, like when he came late to the:
-Kidnapping of Ciel on the 2nd episode
-Kidnapping of Ciel in the Jack the Ripper case
-When the dogs in the Barrymore town were about to attack the servants and Ciel
-When Ciel finally told Sebastian to come for him/escape from the jail
Vincent wanted Ciel to act by himself, even though he had a powerful weapon.
When Ciel's soul was taken from him, he could've gotten furious since the opportunity to be with his while family again was ruined. After Ciel became a demon, his chances of being together with his family were ruined forever. And two demons can't fuse together either. Take Hannah Anafeloz for example, even though the triplets are hers, they still have their own thoughts (like when they thought she had a big rack). This means that the Phantomhives can never be together.
Does this make sense?