Well, I keep a cap on calories and I eat quite strict low carb, but 1200 calories seems really low and extreme and frankly unnecessary and unsustainable, even without exercise, and with moderate exercise as well it's probably in the range of things to make your body think there is a famine & drop your metabolism.
I'd recommend just going strict low carb as a first step - you can log calories so you know where you are, but at least for the first weeks I'd let myself eat what I needed to be satisfied and get into ketosis. After a few weeks if you're not losing the next step would be to share a few days worth of menus on here, see if anyone can identify any problems, and only after that would I move to restricting calories.
And probably your very first step should be to decide what your diet plan will be and get the book for that (and READ it!). There are many versions of Atkins, most of us on this site recommend avoiding using the Atkins products (bars, shakes, candy) and concentrate on just eating real food instead. Most low-carb diet books have very similar starting phases, so don't make yourself crazy trying to figure out which version, just pick one and start & you should be fine.
I'm wondering what you mean by this "I'm eating lower carbs but something isn't going right"?
Lower-carb isn't LOW carb, and I don't know how long you've been at this - plus weight loss in the first several weeks varies a lot from person to person, but you should expect to lose about 10% of the total weight you need to lose in the first 4 weeks - and some of those weeks you'll likely see no weight loss - everyone is different, but many many people lose a chunk, then stall for 2-3 weeks before they start losing again - and the remainder of the weight loss will be slower.
Having reasonable and long-term expectations is a key to success. The biggest difference between people who lose a good chunk of weight and those who don't is HOW LONG THEY STAY WORKING AT IT! Plan to join a few threads to keep your mind in the game for many months, and worry less about how fast it's coming off, and more about how long you'll stay engaged in managing your weight...
There you have it, a nickel's worth of free advice : take what is useful to you, and throw away the rest. Good luck.