"He had a wild entrance, but he's healthy and he's a happy little boy," Carson tells PEOPLE exclusively

Jess Carson-1
Credit: Carla Allen

Jess Carson‘s son Parker gave little notice of his arrival – in fact, the Midland guitarist’s second child was born before he and wife Camille could even make it into the hospital.

The couple welcomed Parker Emmanuel at 9:20 a.m. on Sunday, May 14, in Texas, they confirm to PEOPLE exclusively.

He weighed 7 lbs., 11 oz., and was 19.5 inches long.

“He’s good – he had a wild entrance, but he’s healthy and he’s a happy little boy,” Jess tells PEOPLE. “He’s pretty rambunctious, he likes to keep us on the move.”

Jess says he and Midland have been traveling so much as of late — their single “Drinkin’ Problem” is No. 17 on the country charts — that he was initially anxious about actually being there for Parker’s birth.

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“[Camille] had a 28-hour labor with our daughter Ida Mae, so I was just hoping at the least it’d be a long labor and I could hop on a plane and come back,” he says.

Luckily, Jess was at home in Driftwood, Texas, for Mother’s Day when Camille went into labor in the early morning. Not long after Camille’s water broke, the time between her contractions got shorter and shorter.

Hopping in the car, Jess went into emergency mode trying to carefully, but quickly, make the hour-long trip to the nearest hospital.

“We’re like half-way there and she’s saying, ‘Oh no, oh no, he’s coming,’ ” says Jess. “She calls the midwife and the midwife’s on the phone and she’s yelling at me and telling me to pull over and she’s gonna talk me through delivering Parker.”

Jess Carson-2[1]
Credit: Carla Allen

The musician says “terrified doesn’t begin to describe” his feelings.

Luckily, Parker held out until his parents reached the south Austin hospital’s emergency room roundabout. Jess says he put the Chevy Suburban in park, ran around to the passenger’s side, “opened the door and [Parker] just came out.”

Doctors met the couple in the parking lot, and transferred Camille and baby Parker to the birthing suite. Jokes Jess and Camille, “He sure does know how to make an entrance.”

“Camille was so brave and strong – way more through it all than I was,” says Jess. “That’s why I want to share the story.”

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Jess tells PEOPLE that Parker shares his moniker with his grandfather – Parker’s great-grandfather – a highly-decorated WWII fighter pilot. Emmanuel, Parker’s middle name, is Camille’s father’s middle name as well.

The couple also share daughter Ida Mae, 15 months.

“She’s figuring it out. I think it’s always hard for an older sibling,” admits Jess. “They have 100 percent of the attention and then here comes a newborn baby that needs around the clock care. But my personal relationship with Ida Mae has gotten even more special.”

Despite the craziness of last weekend, Jess says he and Camille are settling into their new lives as the parents of two.

“Our hearts are so full and our little family feels even more complete now.”