As for the question of how Spike could enter the house uninvited, as much as he assumed that he could do so because of the First Evil's growing power and influenc, I thimk that it had more to do with the owner. He didn't just leave, he ABANDONED the house, evacuating Sunnydale, no longer thinking of it as his home. That made the house just an unclaimed building, like Angel's mansion after he and his minions had killed the legal owners.
As for why Buffy didn't just say, "It's my way or the highway for anyone living under this roof," I have no clue whatsoever unless it's because of her eagerness to see herself in the wrong so often, especially when dealing her friends, whenever things went bad.
And in this episode, we see the weakness in Buffy that compares with Angel's own. Whereas Angel seems to take it as fact that he is somehow the ultimate authority in what is the "greatest good," and what should be done to see it come about, even to the point of manipulating his friends' memories, or even alternating time itself, Buffy seems to feel that the ultimate blame for any and everything within her sphere of influence that goes wrong must ultimately be her fault. We will see this, I believe, quite a bit in Season 9, when Buffy wants to take the blame and guilt for everything that Angel, Willow, and Giles did that contributed to the disaster. Granted, she contributed her share, mainly in going all "Kama Sutra" with Angel/Twilight, but the others contributed at least as much, if not far more.
If, as the First Slayer told her, death is her gift, unnecessarily assuming all the blame for bad things happening is Buffy's curse.