Should I keep a cat even if it causing allergy problems with my children ages 2 thru 7?

Depends. Several factors here. I usually never recommend it if the family is attached to the pet, but if it is causing severe symptoms, you should sequester the animal out of the bedrooms and living spaces. Then make sure you thoroughly rid those areas of cat dander as it is a potent and tenacious allergen.
No. Cat allergies in children tends to get worse with time with repeated exposure. It is better to get rid of cats around children allergic to cats.