Frank Sinatra has a bunch of number ones (including apparently the first Billboard #1, I'll Never Smile Again); Nancy made it with These Boots Are Made for Walkin'.
Have any other parent and child both individually made it to number one?
Nat "King" Cole:
Hank Williams Jr.:
"(Just Like) Starting Over" (1980) #1 US, UK & several other countries (plus several other solo hits and quite a few with a band he was in)
"Too Late for Goodbyes" (1984) #1 US Adult Contemporary (plus 2 US Rock #1s)
"Love Letters in the Sand" (1957) #1 US (plus other US & UK #1s but none that were #1 in both, oddly)
"You Light Up My Life" (1977) #1 US, US AC, Canada & Canada AC
The Mamas and Papas hit number 1 with Monday, Monday in 1966 on both Billboard and Cashbox.
One Mama, Michelle Phillips, and one Papa, John Phillips had a daughter, Chynna Phillips, who got together with two sisters, Carnie and Wendy Wilson to form the band Wilson Phillips. In the early 1990's, Wilson Phillips had 3 number one hits (Hold On, Release me and You're in Love)
...and oh yeah - Carnie and Wendy were given their surname by their dad Brian, who had a band with his brothers Dennis and Carl that had some commercial success too.
Late to the party, but I've found another parent-child combo with individual #1 singles.
My mind went immediately to Dylan, but, upon further digging, it turns out he never had a #1 song that he performed himself, even though his son, Jakob had. Even with the Traveling Wilburys, while they had several #2s, no #1s. However, since you didn't exclude writing a #1 song even if they didn't perform it, one could count Dylan's writing of a song that eventually became Wagon Wheel by Darius Rucker.
So, if that counts...
And though it only made it to #1 on one specific chart, I think Willow's song lets her be included on this list as well: