I think cardio is important. You don't have to do it to lose weight, but it's good for your heart and breathing.
I know very well about time constraints! Taking the time to go to a gym is just not feasible, so I work out at home. I don't know if this would help you, but I have a set of resistance bands. They came with a DVD with some circuit training. I do a five-minute warmup (usually just go up and down the basement stairs, carrying 3-lb weights or run in place) and all three circuits in 45 minutes. Each circuit is about a dozen different exercises with cardio in between to keep your heart rate up (hopping from side to side, jumping jacks, or marching in place, depending on your fitness level).
You can do a lot with the bands, like attach them to a door for lat pull downs or rows, but the DVD training is all free-standing, so you can do it almost anywhere. I do the whole workout on a 4 x 4 mat. I do "the plank" afterward for as long as I can (about a minute--working back up to 2+ minutes) and then some stretching. It's a good workout!
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