There are different schools of thought on Atkins, Keto diets, etc. For me personally, I find it hard to go thru a typical day eating extremely low carbs. I also train 6 days / week - I feel like shit & get headaches if my carbs are too low for extended periods of time. Even for a keto diet you get to do a carb up / refeed to support a heavier lifting / training schedule.
To your question of " is 12 min a day really enough" - depends on what you are doing and what your goals are. Because I "like" being in the gym, my workouts will be longer. I can't do anything worthwhile in 12 minutes. If you are talking just cardio, a nice HIIT schedule is a couple of 20 min sessions / week - for ex, hi intensity for 1 min, low for 2 min, repeat for 20 min. This sort of cardio is outlined in the Body for Life book if you are looking for more infrmation. Same with weights - I like training 6 days/ week. I generally split my body parts into muscle groups, 1-2/day, some days w/ cardio, some only cardio. I just switched up my schedule to train w/ some guys who follow Westside Power lifting (see Spatts' "Helpful Links" sticky & the training board for more on this.)
There are many different ways you can go about training & dieting. The primary questions are what are your goals & how will the schedule fit into your lifestyle? If you can't / dnt' want to train 6 days/week, then dont' choose a routine that requires it. If you are just getting started w/ lifting, start w/ a basic schedule of probably 3-4 days of lifting. Cardio - you can do HIIT a couple times/ week, and do a couple sessions of longer cardio on your "recovery" days. It all depends on what will fit your schedule - if it doesn't fit your schedule, you won't do it.
You could follow the same lifting schedule as your husband, just adjust the weights to what you can comfortably lift (while still challenging yourself). Throw in 3-4 days of cardio. Stick to Atkins if you want. It depends on if you have enough energy to train in a worthwhile manner. Or throw in a carb up every 4 days or so. Primarily, just eat clean and enough. Keep the processed foods to a minimum. Get good quality fats (e.g. flax seed oil) in your diet. Get enough sleep.
Again, for an overall introduction to diet , training, cardio, I recommend taking a look at the Body for Life book.