Wow! S., you are young to be a mom to a 15-year-old, and I am sure that it must feel overwhelming at times. I have a 14-yr-old daughter who struggles with being a picky eater (hates most fruits and vegetables), and does not have very good self-control when it comes to sweets and high-fat snacks. We have modeled healthy eating and exercise for her from day one, so it isn't necessarily related to her experience with her mom--although that probably didn't help.
I would imagine this is a tough transition for this teen, and she may be dealing with a lot of emotions right now, and doesn't really know how to handle them. Food is probably a source of comfort for her, which is very typical for females in general. This girl is in a family that is the second one for her dad; this may cause her to feel less-valued at times and a little bit passed around. I don't say this to make you feel bad, but there are wounds for children growing up in this situation. If you and your husband can recognize this, and work on really helping her feel safe, secure, and a valued member of the family, I believe that would be step one. If she feels safe with you, then she is far more likely to open up and talk about her emotions and struggles.
The second step is to continue what you already done with your other kids: model healthy eating. That may require, as you mentioned, not buying some of those things for a while (chips, cookies, etc.). Reserve them for special occasions such as birthdays, meals with company, or celebrations. Even though your other children don't have a problem with temptation, ask yourself: "Why do we need these foods in the house in the first place? Does anyone benefit from having chips or cookies in the house?" If your family is like most, when the food is there, it will get eaten. Removing the temptation is good for everyone!
When it comes to exercise, the best thing you can do is plan family activities and include her. If you want to put up a basketball hoop, plan for you or your husband to be out there shooting hoops with her. Go on family walks, hikes, or bikerides. The options are really endless, but it will take you being involved to make the difference. All of these suggestions do NOT involve you saying to her "I am concerned about your weight," but all of these things can make a huge difference in that teenager's life.
This is the time to establish the kind of bonds that will affect her relationship with food for her whole life. If food becomes a bandaid for wounds, it will take a long time for her to work through that as an adult. She will also be affected in her relationships, especially with men. Your husband will play a HUGE role in all of this, so hopefully he is on-board with whatever way you choose to address this.
I know you have already received a lot of advice, but I didn't see much that addressed the possible underlying emotional issues, and I think that is so important with teens. You have shown that you truly care about her by reaching out for help, and I believe that you will be the kind of mom who can make this family work. God bless and best of luck to you.
I am a SAHM, work part-time from home, and have three children (14, 7, and 5 years).