The lady that owns the Riverwood Hotel has been killing me and she is part of my quest so I can't kill her. I need to talk to her but I can't because she is killing me. What should I do?
You might need to restore from an earlier Save - if Delphine is attacking you, it must be that you have already done something that upset her for instance you accidently hit her with a weapon, or attacked a resident of the village.
There might be a way of correcting the problem, by paying any bounty you have, but going back to an earlier save might be far easier.
Try resting outside of town for a week. This can reset some NPC oddities.
Go to Whiterun and commit a crime. Then pay the bounty or give jail time. Return to Riverwood to find your needed NPC free of any hostile actions.