Is a dehumidifier be a good idea for my mother, who has copd?

Maybe. There are no solid scientific data on dehumidifiers in COPD patients. Most COPD patients feel worse when the weather is humid. Try the dehumidifier, it may help her but if she doesn't feel it is working, return it.
Maybe. If you live in a humid area, it might be a good idea. In a dry environment, a humidifier should be considered.