some great excercises for at home are calisthenics. they'll help with muscle as well as cardio. calisthenics are excercises that you use your own body weight as your weights. when i trained with my old varsity team we did these a few times a week as a group, but everyday on our own.
some items that you could do at home (when no one else is home if you don't want your mom to know that your working out):
-running stairs
if you have a few sets of stairs in the house (or even one flight) going up and down it many times. in my parents house i used to run the basement steps about 100 times (so 50 up, 50 down). best thing is to step on every step, go quickly, but it's ok to go slower if you're getting tired. if you're getting tired, keep going, keep moving, once you finish you're break will feel so much more deserved. don't be afraid to sweat!
-pushups and situps
if you want to break up the stairs a little, after every 10 flights do 20 push ups, 20 sit ups (or crunches). or do sets of them on their own. don't underestimate them. they're awesome for building strength.
-dips
great for building arm muscle. find a bench or chair that is sturdy, face away from it, put your palms on the seat with fingertips over the edge, and bend you knees using your arms to lower yourself slowly toward the ground (til your arms are at 90 degrees), then back up til they're fully extended, repeat several times.
squats
great for the quads (front thigh). with feet shoulder width apart bend your knees as if you are going to sit on a chair, and slowly rise again. it may help to extend your arms in front of you. do not let your knees extend past your toes, as it could result in injury. lower your butt. it's hard to get balance in the beginning, sometimes helpful to have a rail/table to rest a hand on (but not put weight on).
calf raises
stand on a stair with your balls on the stair, and your heels hanging off. raise up on your balls, then slowly lower. repeat. if this gets easy, you can always hold something heavy to make it harder (textbooks are great).
all of these need to be done at a slow controlled pace. they won't be effective if you're using momentum to complete them. also they're very customizable in that you can add more sets and reps and your body adjusts to them. you can also always add weight to make them more difficult too. other exercises like chin ups are in this category too. you can just google calisthenic workouts and get all sorts of ideas. :)
hopefully with time you'll feel comfortable enough to work out when your mom is home. but i know what it's like to have a mom like that. mine was like that. i didn't want to work out around her..... eventually we did weight watchers together, and began working out together, and that helped. but i went for years only working out when no one was home!
good luck, and keep it up. best way to see results is to keep at it. the harder you work, the better you'll feel. believe me. it may feel awful, and like you just won't make it, but if you keep at it, after your body has had a chance to catch it's breath, you'll feel great. nothing like a good workout to build confidence.
tams