I hope that maybe once you move out, you can keep your relationship with your family, just in smaller doses. With a little distance, things can change.
In the meantime, check out MyFitnessPal. It is an app/website where you can track calories in and out. It is a favourite of many folks here. There is no secret to weight loss, just burning more calories than you consume. There are websites where you can calculate your resting calorie burn like
http://www.bmi-calculator.net/bmr-calculator/ or BMr. This will tell you how many cals you would burn if you lay in bed all day! From there you can get an idea of how much under that number you should eat, based on your activity level. Also check out
http://www.losertown.org/eats/cal_act.php. This tells you how long you should expect your weight loss to take based on your calorie intake. Of course it isn't perfectly accurate because we all have stalls and higher oops days but it's kind of a fun tool. At least I thought so. Hopefully it doesn't discourage you! Just remember time will pass whether you're losing weight or not so you might as well give it a go!
I'm sorry you are having such problems in your relationship with your mom. Feel free to come here and talk about it. If you prefer you may also pm me.
Stay true to you and all the best!