It's not that strange at all. You constantly hear Abby speak of her mother. Who's the one she calls when she's in a jam and her spells screw up? Her mommy. That's why she has a cell phone/wand. So they can keep in constant contact with each other. There seems to be that added feeling of character over-interpretation that her mother really manages to look out for her, while Abby remains just a little clingy. Meanwhile, her father is never mentioned. Ever. Not even in any kid's books I know. Sesame Street kid's books, where Sesame Street continuity went to die, and every character has parents that are completely inconsistent. Like we're supposed to believe after years of seeing Grover's (has to be) 50 year old frumpish mom, she's all young and hip all the sudden.This should be most interesting... though, for some reason, I feel that using Abby might be a bit of a cop out, I don't know why.
So logically, this seems to be something to easily retcon, and the best way to do that is to pick out someone who's father isn't already established (imagine how heart breaking it would be if it happened to Elmo or Baby Bear), and a character that's more or less well adjusted (Telly would have very unfortunate implications, given his overemotional highs and lows). Plus, at the approach they're taking, they want a character that's well established enough for kids to care, listen and sympathize. That would be Abby. She's just well adjusted enough to work (though it does add a sad level of over-interpretation when she freaks out about getting a spell wrong).