My albino hatchling wouldn't constrict the first time, all you have to do is tug on the tail a little bit and they'll constrict. I'm assuming my snake didn't constrict because she was used to eating live and if the rat doesn't move I guess she didn't feel the need to constrict. If you're doing any food switching I would try switching to rats, since its more economical.
And same question: why switch to live? mice smell bad and it's much much cheaper to get f/t