Hi there,
I totally recommend the book "Healthy Sleep Habits, Happy Child." Our daughter, like yours, was/is extremely strong willed, stubborn, etc. Cried/screamed at bedtime, etc etc. Same story as you. When we finally put this book's recos to work, it took 3 days max for her to get to sleep on her own. And then we wondered why we had waited so long to do it. The book is incredibly helpful because it explains why you are a good parent when you insist that your child learn healthy sleep habits, no matter how much it pains you to hear them cry. He uses the vaccination/medical attention analogy. You wouldn't tell a doctor to stop a life-enhancing/saving procedure just because your child was crying. Same with sleep. It can't be about the crying. Sleep is about your child's (and YOUR!) good health, mental development, physical development, etc etc. You are doing a good thing when you teach your child to self-soothe and get to sleep on her own. You are preparing her for life in a positive way. Maybe this will help explain it to the grandparents, that interrupting the lesson because she cries is actually not good for the child. He has both the CIO and WI/WO methods. We tried the WI/WO, but our daughter was so strong-willed that it didn't work. She just stayed awake and awake while I was there. CIO worked, I swear, in 3 days. First night, 35 minutes of crying during which I begged my husband to not let me go upstairs no matter what, with tears rolling down my face. Second night, 12 minutes. Third night, 2 minutes and out like a light. Fourth night, almost immediate sleep. Just remember that at this age, your daughter knows she is loved, does not think you have abandoned her, etc, so it's not about that. In our case, it was a total power play by our daughter (which is entirely natural to do), and we were letting her play us to both her physical/mental detriment and ours.
I hope this helps. I will also add that we have had to change her bedtime routine periodically when the standard one has stopped working. It's a bummer that it changes just as you get the hang of it, but that's life with kids. ;) Our daughter went to one nap a day at 14 months. Bummer! And then she stopped napping outright at 3. I was bummed to lose the time during the day, but the bedtimes went so much easier because she was actually tired.
Good luck! And remember while she is crying and screaming and you aren't going upstairs: This will pass, your daughter will be better for it, and your mental health will be better for it. It's misery in the moment, but the payoff is tremendous. You are doing the right thing! Believe that.
E :)