For vegetable stir-fries, I would recommend a nice nonstick pan with any oil of your preference with a high smoke point. You want to cook your veggies with a very hot pan for stir-fries. The order in which you put in the veggies matter, so put in the vegetables with longer cooking times like carrots first, then the other veggies like peppers and peas. For Asian dishes, it is all about having the right ingredients and just practicing. It is amazing how one little ingredient in small quantities can drastically change the flavor of the dish.
Pad thai is actually something I tried cooking for the first time a week ago. Making a home style pad thai is actually not that difficult. I think the hardest part in making pad thai is acquiring all the necessary ingredients. Pad thai has beansprouts, peanuts, shrimp, and other delicious healthy ingredients. There are various recipes, so I can post you a recipe if you are interested.
Do you and your daughter enjoy spicy food? Also, are you familiar with Korean food? There are spicy dishes in Korean cuisine, but not everything is spicy. There are a lot of vegetable dishes and recipes in Korean cooking. One dish people love after trying it is bibimbap, which means "mixed rice". It is a rice dish with all sorts of vegetables and roots, an egg, Korean chili paste, and meat if wanted. Since you and your daughter like sushi, you can give hoedeopbap a try. It is another rice dish where you mix raw fish, vegetables like lettuce, sesame oil, and Korean chili paste together. The raw fish can be tuna, salmon, halibut, sea bass, etc.
You can also try using parsnips instead of potatoes and carrots when they are used in recipes. One would be mashed potatoes. Interestingly, parsnips are related to carrots and have more vitamins and minerals than carrots do. You can add garlic, salt, black pepper, butter, chicken stock, etc. to make it flavorful. You can add whatever you want to it to make it taste to your liking, while keeping it healthy. Spices and herbs actually have a lot of nutritional value, so that is one way to add flavor to your dishes, while keeping them light and/or healthy.
As mentioned before, roasting vegetables is a nice technique to bring out flavor. One other technique is to use alcohol in the cooking process. Alcohol has the ability to bring out hidden flavors because certain flavors are only alcohol-soluble. Tomatoes are a good candidate for this method. When cooking with alcohol, you want to first move the pan or pot off of the stove top and then add the alcohol, so it isn't in direct contact with fire or extreme heat. This should prevent any potential fires.
You can try mixing certain vegetables with already existing dishes that you cook. Have fun experimenting. Cooking is all about trying out something new and having fun with it.
I hope this will help you in some degree. Good luck in the kitchen and getting those veggies eaten.