Hi Bam,
I was exactly the same and I found this works... I when i was young i had the same problem with bad food but after i started excercising right i lost 23 lbs in 4 months. 207 lbs down to 184 lbs. My advice, just start to excercise in the house while your mother is "around" so she can see you are making an active effort. After a few weeks make some comments about food. I barraged my mother with so many facts but never told her to specifically buy anything. Hopefully your mother might start to surprise you with some of the foods you have been telling her about. For example "cooking with olive oil rather than vegetable oil can help lower colesterol". and tinned tuna sandwiches is not very expensive and is a great way to prepare your muscles to burn fat (along with strengthening muscles).
A good thing to target, i found, is thigh muscle and glutes. This should be done by doing a maximum of 12 reps of all excercises, regular squats (for thighs) and sumo squats (legs apart and feet pointed out)(for glutes). building these two big muscle groups for strenght will turn them into fat burners. but I found the key to motivation is "feeling" better so core excercises will help alot and you dont need machines for some of these:
(scroll down a little)
I know building muscle might seem like its going to make you look bigger, and it might but only a little... and only for a little while, but believe me, after a few weeks you will start to loose weight.
Creating STRONG muscle (so holding heavy objects while doing squats and other excercises), drinking 8 to 12 glasses of water a day, eating a full breakfast and doing regular cardio (walking, cycling or jogging), all will help increase your metabolism.
Try starting-off doing those excercises once every three days, eat protein (meat and vegies) straight after a workout. then after a month do the excercises every Monday, Wednesday and Friday. you might not loose weight right away BUT you will condition your muscles to continue to burn more fat even if you get a little lazy a bit later on (like everyone actually does).
This form of excercise can take a toll on your joints, ligaments and tendons so be sure to listen to your body and take it easy if you start to hurt. The MAIN thing you need to know is, if you don't see improvement in time where you think you should, PERSIST! eventually and enevitibly you will.
Its what I did and I had and still have terrific results!
I hope this helps and best of luck! Let me know how it goes.