I think the person standing besides him in the flashback panel is his past business partner or subordinate/supporter which became the sisters' mother. Remembering her because of the photos and Yuu's declaration probably made him relent.I'm too sleepy to give a rational thought. Their dad is pretty dense too. My guy, those smiles your daughters showed in those pics don't look like smiles you give in business partnerships.
I know the series has been losing a little of their shine after namek, but this page for sure gave me a good laugh...Aibou!