diet is NOT the word.
the wordS are "lifestyle changes". and your daughter isnt the one who should be totally responsible for it, you are her parent, you are probably the one involved in grocery buying... so its more about you making the changes for your family....
shes 13. where is she getting ahold of the treats? where is she getting ahold of the starbucks? shes 13, its not like she can have a big job legally, so either you are giving her the money, or she is taking it right? perhaps she has an allowance, that money should be saved in a bank account, and spent ONLY on things that she wants - not on snacks - and you should have control over when and how much she withdrawls, perhaps having your bank only hand over the money with YOUR signature. this might mean you have to be the sole name on the account.
have fresh fruits and veggies available at ALL TIMES. have HEALTHY snacks, portion CONTROLLED prebagged. put refrigerated healthy snacks front and center, so that they are what is highly visible when opening the fridge door.
as far as exersize, you cant tell her "you need to exersize"
its quite possible that she knows, and its quite possible that she is HIGHLY sensitive about her weight already. pushing her to "diet" or "exersize" might only send her deeper into shame about her body.
what you should do is find things that the whole family can do to be active. sign up for a fundraiser run or walk. do a community team sport. take DAILY walks after dinner.
buy smaller plates. research has shown that even if a person is not hungry they will eat most of what is on their plate, and most of the time if its a large dinner plate, that means that the large dinner plate will be FILLED with food, not proper portion sizes. check online for healthy portion sizes of all foods. remember that fruits and veggies should make up OVER 2/3 of the plate, and the "meat" less than 1/3.
breakfasts should be healthy cereals or something like that. just dont buy the sugar ones. its really simple. if chips/popcorn/ice cream and the like are struggles for your family, just dont buy them, who has the money for needless snack foods these days? i know i dont. YES, your family will miss the snacks. but it only takes a week or two for that to ease, and a month to make solid lifestyle changes to improve your health.
if you REALLY want to be healthy, i hear that vegan or vegetarian is really the way to go. cures diseases from what ive heard. :D
get a pur water pitcher, or just any kind of water dispenser for the fridge or house. make sure that it is full of fresh cool water at all times. stop buying sugary drinks like koolaid and pop (PLEASE DONT BUY SODAS!! ugh. even diet sodas are linked to increased eating and increased weight gain, not to mention the dental issues caused directly from soda sipping... and who has dental insurance these days?)
the best way to show healthy eating etc is to do it with them. do your best to have at least dinner together. getting up a bit earlier for a morning walk, and a healthy breakfast together is always a good idea too. by evening people usually want to relax, so if possible getting up early is always good too!
dont get me wrong, im not mrs perfectly fit or anything. these are just things in my head that i TRY to stick to. so just TRY to start with something, and keep these things in your head like i do. honestly, my husband LOVES chips or something crunchy in his lunch. but i know if we have them in the house, one more serving will get eaten after dinner, and as a work at home mom i know i will get into them myself. so honestly, i know i would rather buy 2 pounds of apples for the 4$ than the bag of chips. :D