DD is 18 mths and has been going through this the last 2-3 months, specifically bath time. Like you, we had a great routine, we would say "Is it time, DD?" and she would run to the hallway and dash to the bath. But now she cries pretty much every time and has to be carried to bath by DH. She generally settles after a few minutes and ends up having a lovely bath.
I felt terrible about it but we persisted every night and DH still does bathtime, and she is slowly going back to the way she was. I can imagine this is definitely wearing you down if it is every single task! Actually, now that I think about it, DD usually wants me to do most tasks too - give her bottle, change nappy etc. I think (I hope) it's a phase and soon we will have little Daddy's Girls