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Alec & Hilaria Baldwin 'So Happy' After Welcoming Lucía, Kids 'Excited to Have a New Sibling': Source

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Alec and Hilaria Baldwin (happily!) have their hands full.

The pair welcomed their sixth child, daughter María Lucía Victoria via surrogate, born just five months after Hilaria, 37, gave birth to their son Eduardo "Edu" Pao Lucas back in September.

"For Hilaria, having two babies so close in age is pretty crazy, but she still loves it," a source tells PEOPLE in this week's issue, on newsstands Friday. "Lucía is perfect. She fits right in."

Diapers and double the baby duties aren't the only challenges facing the couple, though. Earlier this month, Alec, 62, announced he was quitting Twitter when he received backlash. And, in December, Hilaria's name began trending online when people claimed she fabricated Spanish roots and a Spanish accent despite being born and raised in the United States. She since apologized for not being "more clear" about her background.

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Despite the social media drama, a source says things are much more pleasant inside the Baldwin household. The couple also share daughter Carmen Gabriela, 7, and sons Rafael Thomas, 5, Leonardo Ángel Charles, 4 and Romeo Alejandro David, 2. Alec is also dad to daughter Ireland, 25.

"Alec and Hilaria are so happy and spending time bonding together as a family. Lucía's big brothers and sister are all excited to have a new sibling," says another source.

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Earlier this month, the mom of six got candid on her Instagram Story about juggling son Edu and newborn daughter Lucía, writing: "Having two small babies is so fun and cute. there are also challenges. like Lucia just had an explosion and I have Eduardo rolling around...so I'm just gonna lay here, covered in poop, entertaining Edu...until I get a genius idea how to get out of this 💩 situation."

In another Instagram post, Hilaria said the family feels "overwhelmed by how fortunate we are" to have their "rainbow baby" Edu, adding of their newborn girl: "We are living each day, bonding, and grateful for all of the very special angels who helped bring Lucía into the world."