I think you should do what took me a few years of experimenting with.
First: Since she's 2, do her hair WHILE she's in the bath. Take a bath with her and have her play while you put her hair up.
Second: Put her hair UP. While years later her curls will be her pride and joy, right now, she's little, and gets into messes and goes to bed like a sleeping ninja. The curls get tangled easily right? You can brush/comb one side and by the time you finish the other side , your previous work is ruined? Put it up. Make braids and ponytails. It gets her hair out of her eyes and trains it to go back.
Thirdly: Don't shampoo everyday. Use only conditioner. Wash her hair on weekends.Try things like Garnier Frutis that has low sulfates and natural oils. Then, as you wash it out, leave a litttlllle LITTLE bit of conditioner in her hair. If it makes it easier, wash it all out then put a small [dime size] amount back in. Curly hair needs moisture and protection but since she's so small, her hair isn't grown up enough to handle the heaviness.
Let her sleep with her hair wet and braided if need be because of time. The water overnight does WONDERS and she'll notice too.
She's small so those little cute hair bands with little balls at the end... those are the devil's work to her. And the Rubber bands, those HURT and snag and tangle! Instead, use scrunchies. Scrunchies can come in lots of colors she'll love and don't hurt.
Hope this Helps <3
If you need to do her hair dry, Bring Johnson and Johnson hair detangler and leave in conditioners that you water down so it's sprayable. The more water, the easier to do. Even just really water-ed down conditioners are great.
Use a BRUSH on her hair. Not boar or paddle or cushion though. Strong wide toothed brushes that have vents are the best on little girls' hair because it keeps curls in sync. It doesn't hurt, and though it's meant to dry, if done in the shower or constant sprays, it allows the water to spread.

Much love to your baby girl and I hope your life with her hair gets better X)