What can i do.............?

well you see, i am just overweight. not a lot, barely but i absolutely hate it. its like theres an extra chunk attached to my belly, plus my thighs, they jiggle and its not attractive at all. someone told me that if i eat healthily and go jogging for 20 minutes every day i will be sorted. well, thats easier said than done. im a teenager and my mum thinks i look fine and wont let me diet. i have an exercise bike in the garage but that makes my thighs appear bigger, i want slimmer. i cant sneak out and go for a jog either as where i live you will have to stop every 2 seconds for traffic and bends and corners or slow down. id rather have a clear space to jog in. there are places but id have to drive there, i dont have a lisence. ive asked my mum to go walking before and she came but she has a real bad leg so we have to stop often and go slow and not go far which is pointless in even going in the fistplace. its just that its summer now and its real hot so i want to wear bikinis and crop tops and shorts but not with the way i look now! so i was wondering if i was to jog on the spot for 20 minutes, go on the exercise bike for 20 minutes and skip for a bit, would i get similar results?