Hi and

to disABILITIES!
First thing is that most lines at WDW are "mainstreamed", so a person in a chair will be able to go through the regular line just as anyone else and will either be in special seating or transfer to a ride vehicle, depending on the type of attraction.
For those attractions where the line is not mainstreamed your group will either be pulled out of the line at a specific point or directed to an alternate entrace at the start. When using an alternate entrance it is usually limited to the person with the disability plus up to five others, so your group of six will have no problems.
As far as her reticence to use a wheelchair here are two suggestions.
One is to pick a location that is about a mile from your house and ask her if she could easily walk there. After a short pause while she is thinking, also ask "and back". And if she is not sure then ask "three times". Once around the World Showcase Lagoon Promenade is over 1¼ miles, and most people find they do between seven and twelcve miles per day at WDW.
And then ask her the following questions. Here are the suggested answers to go with them.
1. Are you disabled (even temporarily)? Yes.
2. Do the people you are traveling with, such as your family, know you are disabled? Yes.
3. Do you expect to meet anyone you know during this trip who may not know you are disabled. Probably No!
4. Do you expect to meet a bunch of people who you will probably never meet again in your life? Probably yes!
5. Is there any reason at all that you should care what these people think about you? Absolutely No!!
6. Will using a wheelchair or
ECV make for a better vacation for
you and your family? Absolutely YES!