For Yahiko, he had two reasons for accompanying Nanako to Oskia.
First, he didn't want to shock the Japanese public by appearing with fully regrown functioning legs.
As for the second, he wanted to help his daughter marry Charlie.
Nanako was certainly motivated by true love to leave Japan, so she wasn't blushing from her father's encouragement—it strengthened her resolve.
Moreover, her father was clearly not holding back at all.
He certainly wasn't worried if Charlie would let Nanako maint