I'd look again at the pediatrician's thought that it's "normal for her" to go every three days. No, it obviously isn't! It's not normal for anyone, and besides, she's so uncomfortable, is telling you she has that feeling of needing to go (unusual in a 2 year old), and she's changing her eating habits because she is full and bloated. When feces build up in the colon, it's the start of many other diseases as well, so you want to get the jump on this before more and more "sludge" sticks to the wall of the intestine and creates more problems. In addition, potty training is impossible with a child who's already so uncomfortable during bowel movements. That's part of the reason they start holding it in - because they know it's going to hurt. But of course that only compounds the situation.
Take her off bananas for now, and cheese. Try to hide veggies in other things - like sweet potato pancakes (use any latke recipe but use sweet potatoes or at least half & half white & sweet), give her cut up veggies to dip in hummus or ranch dressing (kids love to dip! Make your own hummus if the store-bought is too spicy), add beans (mashed up kidney, pinto, navy) to anything you can (like burgers and meatloaf and falafel patties or nuggets which kids love). There is also a patented kids' supplement that can be added to water or the almond milk that will give her additional nutrients (which helps when she's spitting out the veggies!) and help regulate the colon. I have a lot of friends who have seen a huge change in their toddlers and they've been able to skip all those elimination diets and have much more comfortable children. Something patented has been through so much more testing and is proven safe and effective. Very few food products can achieve patents. There's an excellent one available on line direct from the manufacturer.