It has the potential to be, but it's not what she'd expect, going on secondhand information about Esme and Carlisle. She's not competitive. Edward can have as many mothers as he wants. He can start a collection. Just as long as he doesn't start keeping them all in glass cases in his basement, because that would be inconvenient and sort of creepy.
That surprises a laugh out of Edward. "I don't know if 'mother' would be the best way to describe the relationship, anyway, except for convenience's sake, inadequate words for the odd configurations that crop up in covens - we often presented that way, but just as often I posed as her brother. Once as her nephew. Carlisle I do have more of a filial feeling for, and she's his wife, in addition to being a generally motherly person."
"I am perfectly happy to share being your parent with Carlisle."
(She probably would be even if Edward's original father had been remotely adequate, but since he wasn't, there's no feasible competition for the title.)
"Well, there wasn't exactly a vast selection on offer at the time. But if there had, I'm pretty sure I still would've gone with him."
Because motivating them to save Edward's life would definitely have been on the agenda.
She shrugs. "I would've found out how to get them to, anyway. Carlisle was easy; if you poked him with something sharp, altruism would pour out. Metaphorically speaking. I understand you folks are pretty much impervious to sharp objects and there's not much pouring going on when you aren't."
"Quite impervious, not particularly liquid," agrees Edward. "He did require prompting, though. I was the first person he turned, and he'd had prior chances. He wasn't sure it was right to do that to someone. I wasn't either, for a long time. Bella, of course, could convince me that the sun was blue and the sky yellow."
"But he didn't exactly take much of a push once I put the idea in his head. Convenient, that."
"Very. Occasionally I wonder if he would have eventually broken and gone looking and I'm not sure. I tried to go away from Bella, once, when I was afraid I'd snap and drink her blood; I lasted less than a week. Carlisle didn't have that concern to hold him back and he managed, for years, until a sheer coincidence put her in his path."