Hey Leah ,
You are doing whatever you can . Dont ever feel like a failure. Every Child is Different. To give you an Example, our child was born Premature , and was able to get off the bottle by 16 months.
I never read anything as to how I need to let him get away from his bottle ( Dr Browns

) Hope My method helps you .
I gave him his milk in his bottles and started his water in his Sippy cups.Took couple of weeks. when he got comfortable . then I gave him juice in the sippy cup and water. he was still having milk in the bottle. Then slowly I gave him one serving , in the sippy cup. he had a little. Dint finish his milk .
Then got used to the siipy cup .
Now he off the bottle completely. He is 19months. He is drinking milk from sippy cup , but now he drinking water from regular cup and straw.
Thats is how I taught him the transition.
Leah , I was not born here. I am from India. I have adapted to this culture and learned things from this wonderful country. I watch your show and you are an incredible person. I was in the Dr office with my SOn and watched your show. When Ur daughter was crying and I saw u cry , I saw u as a different person .
U are an awesome MOM.
You will be able to overcome this SMALL herdle .
Hope this helps
Love
Neethu