In here we have Phillip McKeon and Nancy McKeon, brother vs sister, going head to head with Alice against The Facts Of Life.

https://www.sitcomsonline.com/boards/showthread.php?p=6413346#post6413346

Are there any other instances of something like this?

Martin and Charlie Sheen were timeslot rivals when Spin City aired Wednesdays at 9:30 against The West Wing.

I had tried asking this to ChatGPT. It didn't come up with the Martin and Charlie Sheen connection. I guess it was restricted to siblings.

The closest example with siblings was with brothers Dick Van Dyke and Jerry Van Dyke during the 1965-66 season.

The Dick Van Dyke Show's final season aired on CBS on Wednesdays at 9:30pm.

My Mother the Car aired on NBC on Tuesdays at 7:30pm.

There have been a few times when siblings have had overlapping shows, but those were on the same network. Justine Bateman was on Family Ties on NBC while Jason Bateman was on It's Your Move and later The Hogan Family. Kirk Cameron was on Growing Pains on ABC while Candace Cameron was on Full House. Emily Deschanel was on Bones on Fox while Zooey Deschanel was on New Girl.

Veronica Cartright was on NBC's Daniel Boone for the 1965-66 season while her sister Angela began on CBS's Lost In Space, but I don't know the days of airing or the timeslots.

Veronica Cartright was on NBC's Daniel Boone for the 1965-66 season while her sister Angela began on CBS's Lost In Space, but I don't know the days of airing or the timeslots.
Lost in Space aired Wednesdays at 7:30pm ET, while Daniel Boone aired at the same time, but on Thursdays.

Jim Nabors started Gomer Pyle in the 1964-65 season. From December to the end of the season, Nabors was also in 11 episodes of "Valentine's Day." Valentine's Day was on Fridays at 9 ET on ABC, Gomer was on at 9:30 on CBS.

Maybe it happened in daytime in the soap opera world, especially in the heyday of soaps. How about a husband on one show, his wife on another? Doesn't have to be a blood relative. And some soap actors did tend to jump from show to show.

Or how about game shows. Did maybe Tom Kennedy and Jack Narz ever battle it out?