I have written a children's book and also illustrated it. However, I have asked a graphic designer to redo the images for me. I hired her through a company which affords me total rights to the new images. My question is do I list my self as the illustrator on the cover? I would like to add her as co illustrator however I am concerned about implying that she also has rights.
Nope. Not on the cover, or inside the covers, or on the back unless you tell the story about how you tried it first in an "Author's message" like you did here.
Naturally, your question will be answered differently by those in different jurisdictions.
Ethically, you are not the illustrator if you did not illustrate the published work and should not accept credit for work that is not created by you. You are a client of the illustrator's employer. You are a purchaser of a kind of royalty-free (?) exclusive use (?) artwork.
You'll have local laws and a contract that stipulates "rights."