if she's fat, the kids may have been sneaking her food. you'll never know that. does she have toys that keep her active? like a fuzzy thing on a spring hanging from the door frame, that she can do while you're gone?
or one of those balls in a circular open ring that they bat at but can't get the ball out of. anything that keeps her moving will do. try rolling a wadded-up piece of aluminum foil. the other solution (ALWAYS worked for me) is another kitten. they keep each other occupied all day, every day. nobody gets fat. and nobody gets lonely while you're gone to work.
i always had good luck with a spray bottle. i only misted, but that was enough. i also said 'no' in a very firm voice. keep the nails short so it's hard to get a grip on tabletops and be prepared for wetness, especially on kitchen floors. very slippery. but they do learn. another thing they hate is when you blow gently in their face.
edited to say this: she may really only want to be near you. she may need to spend more time with you now that the house is emptier. and some cats are "needier" than others and need more attention, so this may not be a food thing at all.