What have been some musical acts that have brothers, sisters, fathers, sons, cousins, etc. in the act? Off the top of my head I can think of Oasis (brothers), Sonny & Cher (husband & wife), Donnie & Marie (brother and sister), and a few others.
The White Stripes. 
The Kinks
The Black Crowes
Ike and Tina Turner
AC/DC
Marshall Tucker Band
Creedence Clearwater Revival
Allman Brothers
Statler Brothers
Bee Gees
The core of Halestorm is vocalist Lzzy Hale and her brother, Arejay, the drummer.
Maximum the Hormone’s Ryo and Nao Kitakawa are also brother and sister. Ryo’s vocals and Nao’s drums.
Steam Powered Giraffe is primarily David Michael Bennett and his twin, Bunny. Both are vocalists and multi-instrumentalists.
A sort-of case
The current permanent members of the brilliant green are vocalist Tomoko Kawase and bass/rhythm guitarist Shunsaku Okuda, who are married - but they weren’t married when the band started - they didn’t get married until the band had been together for 6 years.
The Hales, Bennetts, and Okudas are also the main songwriters for their bands. I’m not sure who does the songwriting for MtH.
Beach Boys (three brothers and a cousin)
Gentle Giant (three brothers)
Oh - Kings of Leon - 3 brothers and a cousin…
I think this is pretty common:
Ann and Nancy Wilson of Heart, of course
The Sales brothers (Hunt and Tony) in Tin Machine (among other acts)
The Farriss brothers of INXS (three of them!)
Simon Townshend has played with the Who, but I’m not sure how much he and Pete have played together.
Nelson consists of brothers Matthew and Gunnar.
The Bacon Brothers members include Kevin and Michael.
Simon Townshend has been part of The Who’s live act since 1996.
Van Halen - Alex and Eddie are brothers.
And Eddie’s kid Wolfgang.
If you limit it just to brothers/sisters named Wilson, there’s Brian, Dennis, and Carl of the Beach Boys; Ann and Nancy of Heart; Cindy and Ricky of the (early) B-52s; Matt and Dan of Trip Shakespeare; and Carnie and Wendy of Wilson Phillips.
The Carpenters were brother and sister. Captain and Tennille were/are husband and wife.
Then there’s the Jackson Five; Hanson; the Jonas Brothers; the Smothers Brothers; the Marx Brothers… (okay, maybe they’re not a band)
Chevelle; there are a couple brothers in the band.
Oh. Bands.
Never mind.
The Breeders had (has?) twin sisters Kim and Kelley Deal.
Sonic Youth had husband and wife Thurston Moore and Kim Gordon. Timbuk3 was husband and wife Pat and Barbara Kooyman MacDonald. Both couples have split up.
Talking Heads had husband and wife Chris Frantz and Tina Weymouth.
Phil & Friends frequently features his two sons (Grahame and Brian). Caught them at Gathering of the Vibes last year and it was fantastic.
The Tedeschi Trucks Band is fronted by Susan Tedeschi and Derek Trucks–supported by members of their solo bands.
Barlowgirl - sisters
Meg & Dia - sisters
Smoosh - sisters
Blondfire - brother and sister
Orbital - brothers
Stone Temple Pilots - brothers
Arcade Fire - brothers
Radiohead - brothers
Jet - brothers
Biffy Clyro - brothers
Ace of Base - brother and sisters
The Corrs - brother and sisters
The National - two sets of brothers
The Veronicas - twin sisters
Tegan & Sara - twin sisters
Evan and Jaron - twin brothers
Good Charlotte - twin brothers
The Breeders - twin sisters
Blonde Redhead - twin brother & sister
Airbourne features brothers Joel & Ryan O’Keefe.
David & Frank Potvin are the nucleus of both Lyzanxia and Phase 1.
Every Time I Die are, at their core, brothers Keith & Jordan Buckley.
Baroness has brothers Brian and Allen Blickle.
Kim & Kelley Deal were/are both members of both/most/all incarnations of The Breeders. (The band’s history is complicated and includes a few breakups/long layoffs.)
Pete Fitzpatrick and cousin Brendan are both members of Clem Snide.
Death was comprised entirely of brothers David, Bobby, and Dannis Hackney.
Devo features Mark and Bob Mothersbaugh.
Evile is led by brothers Mark & Ol Drake.
Ian & Ruth Underwood (husband & wife) were both members of Frank Zappa’s band(s).
The Gap Band was pretty much just brothers Charlie, Ronnie, and Robert Wilson.
I could continue to look thru my shelves of music, but since most of those entries were just going thru the A-G part and remembering a few off the top of my head, I think it’s fairly obvious that it’s really not that unusual a phenomenon for family members, even married couples, to be part of the same band.
Lynyrd Skynyrd
I believe Abba was made up of two married couples.
The Mills Brothers
It’s a Beautiful Day (David and Linda LaFlamme, husband and wife)
Renaissance (original version had Keith and Jane Relf, brother and sister)
The Cowsills
Sparks (Ron and Russell Mael)
Spirit (Guitarist Randy California was the stepson of the drummer, Ed Cassidy)
Wings
Plastic Ono Band
Sly and the Family Stone had Sly, Freddie and Rose Stone.