I have several suggestions. I am not an expert but I am a dancer and a new mom so I'll offer some thoughts that I have. The main thing I think since you are so busy is to find easy ways to fit in exercise and healthy eating into your daily routine
1. Take the twins for a walk in the park or around the block and walk at a fast pace.A couple times a week or every day if possible.(Wear weights or jog when this gets too easy)
2. Instead of trying a complicated diet try eating healthy food and don't even buy the tempting foods. For snacks eat things like fruit or nuts and raisins and bring these things with you to work. If you are not packing your lunch you could try that as well.
3. Do small exercises (sit-ups for example) while you watch tv. Maybe during one commerical break you do sit-ups and the next leg lifts...Each week do a little more (if you did 10 sit-ups try 20 and so on) As the twins get older may be you can involve them as well.
4. Lastly, look for an exercise class. Even one day a week would be great if you can do it. I have seen yoga classes at NOVA for Moms and babies. Or get a sitter for that one night and get some personal time.
Well S., that is what I can think of with out knowing your situation in more detail. I hope it helps. Whatever you do I think the key is to make it part of your life and not try and go crazy with a fad diet or exercise program. What I am suggesting is the slow and steady way to lose weight. If you want something quicker then you need to add more exercise.
Good luck
E.