If the badge was refused about the time that Motability car was changed then she shares the same problem that I had when the county council would only offer me a badge for the 3 months remaining till the exchange. It was resolved when I managed to find the original letter from the DWP advising award of Mobility Allowance. The fact that she has a car from Motability suiggests that she is in receipt of the Mobility Allowance and hence is entitled to the Blue Badge.
Let me know how she gets on - I'll give you my email address if you want to get in touch