The most important factor for your milk supply is drinling plenty of fluids. Every time you turn around you should be drinking water. When adding excercise to your routine after a long period of not excercising then you need to really up your water intake. Since excercise causes you to sweat, that takes away water that would normally go to making breastmilk. Making breastmilk uses up water your body would use for everyday functions (everyday-type sweat, urine, saliva, nasal mucus... you get the idea). So, you have to replace the water your body uses for everyday functions which has been used by making breastmilk and excercising, AND drink more to keep up your milk supply. Yep, a lot of water. So long as you are constantly sipping on water, you're fine. You don't have to be chugging it all of the time :)
If you have read the Adkins book, there should have been a section on breastfeeding. Even Doctor Adkins does not recommend this diet (or atleast don't cut out all of your carbs) for pregnant women or nursing moms because you need the calories provided by the carbs for your growing baby and producing milk also requires lots of calories.
My husband and I did Adkins for a while before we got pregnant. It really isn't a long-term diet plan. Since I couldn't/wouldn't follow it, my husband stopped, too. In about 4 months he gained back about 25 pounds (half of what he lost). He ended up gaining it all back. Even in Adkins you will be adding carbs back into your diet, just not as many as you had been eating before. If you choose Adkins, you do need to monitor your ketones to avoid ketoacidosis or ketosis (both very similar, just slightly different names).
Weight Watchers is the best diet (which actually means eating lifestyle, I believe). It teaches you how to eat a balanced meal in healthy amounts. Combined with proper excersise, you will not only lose the weight you want, but will learn how to keep it off.
Good Luck!