I don't feel Lwaxana was really so strong, it's like her stories were so focused around her trying to find a husband, and trying to set up her daughter, that was like most of her identity. I never liked Lwaxana, I always felt she was vain and self indulgent, and didn't really care about how she made other people feel, obsessed only with her own pleasure, and thinking she (and Deanna) just needed to find the right man to fix her problems. lol it probably doesn't help I feel Deanna's relationship with Lwaxana mirrors very closely my own relationship with my mother, I guess I find her just a little triggering.
She is also from a planet that appears to be portrayed as something approaching a matriarchy...she’s royalty after all, and in some respects, all that husband stuff and hassling deanna ties into that. She doesn’t just want grandchildren, she wants an heir. When the facade slips with Odo in Ds9, then the less public face is really seen. I am not the biggest fan of Lwxana, but she has a lot going on.