Fic 1: Blaine goes to live with Burt and Carole after his parents kick him out. I've gone through the kicked out/taken in tag and it isn't there. It was on ff.net and it was quite a long, and extremely funny, story.
I remember Carole adopted Blaine so there wouldn't be any problems if Kurt and Blaine wanted to marry in the future. The boys did end up getting married when they went to Nationals in NY. Blaine was living in the guest room, and then he moved into Kurt's room when they got back. Blaine's dad turned up at graduation and Burt got kicked out after punching him. Kurt and Blaine were constantly having sex and annoying the rest of the family, and I remember a scene where they nearly burned the house down as they'd lit candles and one of their shirts landed on a candle.
EDIT: Found by leap_year_baby Awkward Situations: http://www.fanfiction.net/s/7789596/1/Awkward_Situations
Fic 2: I think this one was also on ff.net and was a long one shot. It started with Kurt and Finn trying to come up with a name for their new baby sister (which I can't for the life of me remember!), and went on through her childhood. One scene I do remember is when Blaine breaks up with Kurt and she speaks to Blaine on the phone and tells Blaine to stop making Kurt cry. It was a very sweet, funny and touching story.
EDIT: Found by kksuig Family Ties: http://fanfiction.net/s/6495249/1/