You are correct in your interpretation of the language as to the responsibility. However, neither you nor her have to be the one to actually pick up the child. You are able to arrange for someone else to pick the child up on your behalf.
The person should be someone the child knows and is comfortable with (aunt/uncle, grandparent,.....) It is recommended that is there is conflict between a person and a parent, a different person is used, though it is not required. This tends to be the case with the new significant other being the one to pick up the child and the parent has an issue with the use of the new boyfriend/girlfriend getting involved.
Courts do this to prevent children from being returned to empty houses or other situations due to transportation matters.
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