My sentiments exactly.
I don't know what the family's emotional needs are, and maybe somehow she makes it work on thirty minutes a day, but I don't consider it ideal for a parent to be absent that much (whether it's mom OR dad). I'm also confused as to why she would rather be at a club or PTA meeting instead of with her family given how little time they already have together. Only she would know.
My PERSONAL opinion is that no, 30 minutes a day is not conducive to a strong parent-child relationship.
All I can think is that she's constantly in "resume" mode. If it can be put on a resume, it counts. If it can't, it doesn't count. Unofficial time with family (trips to the park, etc) can't be bullet points on a CV, so maybe it doesn't feel like "real" parenting time to her.
ETA: It could also be about a sense of structure. To me, the scariest thing about the idea of being a SAHP is the fact that I have a bit of a free-falling feeling as I try to figure out how to structure and spend my time with Joe. I take comfort in the structure of my limited work schedule. It's easier for me to meet objectives set forth by someone else than to attempt to make and follow my own. Maybe she can't handle even the tiniest bit of unstructured time? Maybe she literally doesn't know what to do with herself when she's at home?