Everyone of us would like to have our parents forever. There's no end to the good advice they could continue to give us. But, what Mike was also talking about was the need to get all the political, etc. relationships on solid ground. That's why he needed more time. There is also another exchange in the novel in which Mike tells Tom that he can no longer afford the luxury of excluding Tom from family doings.

As far as Mike being uneasy at the funeral, any impressions about that should have been dispelled by his adroit handling of Tessio in his conversation with that traitor. If Mike was uneasy, we should all hope for that kind of unease.