I really feel like she needs to be more punishable for what she is capable of. You can't target her but she can just cast abilities and attack you like it's nothing. Albeit, she really needs another champ to be useful AT ALL, but she'll always be with a champ until they die and later on, she just hops back and forth from teammate to teammates like a poltergeist. You can't punish her in the laning phase, unless the player is just braindead, which is not possible for any other support. I believe that this fact is the number one reason players hate playing against her and the number one problem with her kit. I think that these ideas are good for fixing it. They're not the best but I'm trying to take and give without being too biased:
1) Make it to where she can't anchor herself to a teammate that is below a certain health percentage or if she herself is below a certain health percentage.
2) Make it to where either her health OR mana is slowly consumed for the amount of time she is anchored, if it's her health then make it to where her Q has healing properties similar to soraka's when you land it. If it's her mana, same thing with her Q but instead of health, she regenerates mana.
3) Make it to where she can't use her abilities for a short window after casting her W.
4) Don't give her a free rank in W at level one because her and her target get bonus damage stats when she's anchored.
5) When her anchor is stunned, Yuumi can't cast abilities for her anchor until the stun wears off?
I mean, these are just some thoughts and ideas I could come up with that don't take away from her overall kit but makes her more punishable and less annoying to deal with.