The child actually will not be eligible for more money just because this happens. When a parent goes to school, the child still reports the number in the family in college as just themselves (or any other siblings in the household in college as well). Parents do not count on the child's FAFSA as someone in college, even if they're attending. However, when the parent fills out a FAFSA for their own financial aid, they do get to include the child as part of the number of family members in college. So - student and parent are going to college. Student reports number in household in college as 1, and parent reports number in household in college as 2. It used to be different, but for quite some time this has been the case. The justification from the feds is partially that often parents are only going part-time, not full-time, and it's less of an impact on the family for a parent to go to school than it is a child. Think of that what you will, but them's the rules.
Though, it's quite possible that in the quoted case, the student qualified for Pell Grant money simply because her mother was earning less income due to being a student and that impacted her Estimated Family Contribution enough to make her grant-eligible. That *would* reflect in the FAFSA, though the Pell Grant wouldn't have had anything to do with mom going to school, just the reduction in income.
I have heard of some schools making a professional judgment to factor that extra parent going to college back into the FAFSA calculations. That's one example I mentioned about, in my opinion, some financial aid administrators making potentially questionable professional judgments, because the federal regulations are quite clear on this - parents going to school cannot be reported as part of "number in household attending college" on the FAFSA for the student. I'm not quite sure how a FAA would justify that judgment if they were audited.
I actually went to college the first time when my oldest was a senior in high school. So we were in college at the same time for a year. I thought she might get extra money, but she didn't and I didn't. It does help that we will have two in college next year, but not much.