Dear LnL
I think the parenting bit is so hard, not just having no backup but other parent promoting completely opposite values is very confusing for a child. Is it possible to arrange a meeting with your H to discuss the values you want your child to grow up with or would that just be a waste of time? As you are the constant in her life she will learn from you and follow your example and in her own time choose her own set of moral values. You have the strength and all those other lovely qualities to steer her path no matter what confusing signals she is getting from her father. There is bound to be resistance - it is unavoidable even in the most stable environments, and when she is a grown up she will be very grateful for your strength.... in the meantime (I hope this is true) the more confident and happy you are the more she will be.