I don't think it would make you a terrible mother at all, but there are other options you might try.

If you can get one bottle pumped between feedings and whatnot, then you can feed it to her in place of a morning feeding and you can probably pump two bottles in it's place. You can save one for feeding during the next morning's pumping session, and freeze the other one. I built up a stash by doing this every day for a month. I use the Lansinoh bags which you can freeze like flat little envelopes of milk. They thaw easily by running under warm water. That way you have it for emergencies or sitters or what have you and you don't have to worry about leaving fresh stuff, or it going bad or whatever.

I'm kind of getting too much saved up right now, more than I feel I have room for, but when she goes through growth spurts she can sometimes use 2-3 more feedings per day than she usually takes, so it's good to have it for daycare. Good luck!