Peter's mother was the lovely Valerie, played by white-skinned Anne Reid:
http://coronationstreet.wikia.com/wiki/Valerie_Barlow
Val was indeed electrocuted by a faulty hairdryer plug in 1971, on the day before the Barlows were supposed to emigrate to Jamaica. She was getting dressed for their going-away party in the Rovers, and was just off the phone to Ken who was hurrying her up. The maisonettes where they lived were demolished after a fire (the storyline had been conceived to write them out as the cast wasn't big enough to fill them) and the warehouse and community centre built.
Ken moved into No.3 (later the Bishops house) and tried to raise the twins by himself for the better part of a year, at one point hiring a nanny, before packing them off to Scotland to live with Val's parents. The early 70s was when he racked up most of his girlfriends as he planned to re-marry and send for the twins once he'd found them a new mother, ending up married to the wholly unsuitable Janet Reid in 1973.
Seven actors have played Peter:
John Heannau (1965-70)
Christopher Dormer (1970-1971)
Mark Duncan (1971)
Linus Roache (1973-1975)
Joseph McKenna (1977-1978) - the only one with a Scottish accent!
David Lonsdale (1986)
Chris Gascoyne (2000-2015)