THE PARENTS: Kim Stephan, 38, and Kate Stephan, 45, of Queen Village

THE CHILDREN: Kai Edward, 10; Phoebe Louise, born Dec. 19, 2019

THE BABY’S NAME: Before Kate’s mother died, she predicted they would have a girl; “Louise” is Kate’s mother’s middle name, and “Phoebe” was inspired by singer Phoebe Bridgers, whom they heard at a WXPN music festival.

Kim’s conundrum gave a wrenching new twist to the word “wedlock.” She and her ex had wed in New Hampshire before same-sex marriage was legalized in Pennsylvania, but when that two-year union broke up, she couldn’t get a divorce here because the state didn’t recognize her marriage.

Meantime, a long-simmering attraction between Kim and Kate — both belonged to a circle of Mount Airy friends who got together for monthly potlucks or to watch The L Word — had sparked into a relationship. They wanted to marry. But Kim was stuck in legal limbo.

“It was rough. That’s when I felt the most neglected, as a gay person, in my life,” she says. “The day after same-sex marriage became legal [in May 2014], I went to City Hall to apply to get divorced.”

She and Kate were already living together, along with Kai, Kim’s toddler son from her previous marriage, in a Queen Village townhouse. And Kate had proposed — an elaborate ruse involving fake tickets for a “members-only” holiday bash on a weekday at World Cafe Live. Kate got a haircut, bought a dress, and prepared a small journal for Kim, with anecdotes about their relationship. She glued some of the pages together and cut out a hole large enough to cache two rings.

When Kim — a tad suspicious because parking around the venue was plentiful — entered, Kate was on the stage and Jessica Sonner’s “Rescue Me” was playing on the speakers. “I thought: What did you do?” Kim remembers. “I read through the little booklet she’d made, we put the rings on and danced to ‘You Are the Best Thing,’ and drank champagne.”

That was December 2013. In May 2014, Pennsylvania legalized same-sex marriage. On Sept. 27, Kim’s divorce came through; two weeks later, she and Kate wed — an intimate signing of a Quaker marriage license at 10:10 a.m. on Oct. 10, followed by an evening ceremony and dinner at the Magic Gardens and, two weeks later, an exuberant Halloween-themed block party.

“We talked about kids as more of a dream … like what we would do if we had a daughter,” Kim says. They tried, doing at-home inseminations with sperm from the friend of a friend, for six months, with no success.

“Then we kind of fizzled out,” Kate says. “We decided we would save our money, take Kai on vacations.” But in 2018, Kai began spending weekdays with his other mom, who lives in a high-quality school district in New Jersey; he was with Kate and Kim only on weekends, and they missed the primary parenting role.

They found another donor — a different friend of a friend, this time — and worked out a contract indicating that he would be available to answer questions or meet any offspring that resulted. Again, they tried at-home inseminations: January, February, March.

“Kim was pretty sure she was going to get her period, and then one day she called me and said, ‘When are you going to get home?’ ”

The pregnancy test was positive. The pregnancy itself was miserable. “I’m not a big fan of being uncomfortable,” Kim says. “I was throwing up in my office. I was always tired.” They told Kai with a letter “from the baby,” penned by Kate, that announced, “You’re going to be a big brother. … I’m going to be your little brother or sister.”

Kim, who had been the birth partner for her sister and for her ex-wife, felt frightened of the pain of labor. When the baby was measuring large, they decided on a scheduled induction at Jefferson University Hospital a week before the due date.

That was the kick-start to a night and day of contractions, an epidural that wore off as she reached eight centimeters’ dilation, an excruciating level of pain, a fever, and an anxiety attack that frightened both women.

“Kim pushed a couple of times, but nothing really happened. The baby’s heart rate was over 200. They had to get her out. I was just scared: What if I lose Kim? If I lose the baby? If I lose both of them?”

Phoebe was born at 11:17 p.m. and whisked to the NICU for 36 hours of antibiotics. Kate stood in the corridor, in tears. Kim lay on the operating table, foggy from anesthesia and asking repeatedly, “How big is she?”

After that, everything got easier. “I hadn’t been worried about the mommy-ing part, just the pregnancy part and getting her out,” Kim says. It helps that this is her second lap as a parent; it helps that she is 38 instead of 27.

“I savor parenthood a little bit more than I did when I was parenting Kai as a newborn. This is going to be my last shot.”

For Kate, though, the learning curve is new and steep. “I was a preschool teacher, I worked at St. Christopher’s Hospital, and I come to find out I don’t even know how to feed a baby a bottle.”

Phoebe is starting to laugh, at her mothers, at Kai, at their dog. “We’re working on tracking skills, tummy time, and head control,” Kate says. She often feels tugged between “someday” — eager for the days when Phoebe will play with rattles or shoot basketballs with Kai or learn to read — and the sweet, fleeting now.

“I’m excited for her to get more alert and engaged, but I’m trying to savor every moment we have with her at this stage, too,” she says.

For both women, the notion of family has branched: there’s Kate’s dad in Australia and her stepfamily in Delaware; Kai’s other mom and her partner in New Jersey; his donor; the kids’ multiple grandparents on both sides; and Phoebe’s donor, whom she may someday meet. “It’s a crazy, blessed family that we celebrate,” Kim says.