No, tomatoes are not in the apple family.
Tomato's True Family
Tomatoes belong to the nightshade family (Solanaceae). This family includes a wide variety of plants, such as potatoes, eggplants, peppers, and tobacco. This is clearly stated in multiple sources, including Wikipedia which describes the tomato (Solanum lycopersicum) as "a member of the nightshade family". https://en.wikipedia.org/wiki/Tomato The FruitGuys website also confirms this, stating that tomatoes are "a member of the nightshade or Solanaceae family, which includes eggplants, potatoes, tobacco, and peppers." https://fruitguys.com/blog/history-of-tomato/
While tomatoes and apples are both fruits and may be used together in some recipes (like the Pennsylvania Dutch Green Tomato and Apple Datsch), their botanical classification is entirely different. https://www.hagenbuch.org/pennsylvania-dutch-cooking-green-tomato-apple-datsch/ Apples belong to the rose family (Rosaceae).
Examples of Tomato and Apple Combination Recipes
Many recipes combine tomatoes and apples, highlighting their culinary compatibility despite their different botanical families. For example, several websites showcase cucumber and tomato salads, which often include apple cider vinegar in the dressing. https://meaningfuleats.com/marinated-cucumber-tomato-salad-gluten-free-dairy-free/ https://theforbesfamilyfarm.com/cucumber-tomato-salad/ This demonstrates that apples and tomatoes can be used together in dishes despite not sharing a botanical family.