Thought your post was worth personalized advice and that's why i splitted it!
I think we'll need more info here, that is, what is her wake up hour, meal times, etc (her short morning nap might be due to hunger). Also, your daughter is old enough to transition to one nap and her signs are pretty clear on that (taking one short nap and a long one). By knowing her wake up time we could work on a one nap schedule to help her sleep that one for 2 hours and hence not needing a second one and being rested for bed time.
If she's rested then we can tacke the sleeping on her own issue. One thing at a time. It might turn out that she's overtired and hence the trouble setting. If whe work on her timings then we can work on the independent sleep thing.
When you say you have trouble keeping routines, you mean each person that takes care of her does things "their way"? it is important for little ones to do things routinely, otherwise all your hard work in sleep training gets lost because of the confusion they can experience. It is very important that every person that takes care of your dd is "on board" with the sleep training and the routines cause it's more likely to reach full success that way. We can do that by designing easy to follow wind down and putting down routines that everyone can adapt to.