"At this point, I'm starting to think I'm being attacked for who I am and no answer is the right answer," Hilaria Baldwin said

Hilaria and Alec Baldwin are addressing claims that she fakes her Spanish heritage, allegations that went viral on social media over the weekend, and touched off criticism of her for cultural appropriation.

Last week, Hilaria, 36, began trending on Twitter as social media users — including journalist Tracie Morrissey and Twitter user @lenibriscoe — dug into her past, alleging that she fabricated Spanish roots after having been born and raised in Boston, Massachusetts. Additionally, Morrissey and @lenibriscoee and claimed to have evidence that the accent she often uses is not real.

Hilaria soon addressed the speculation about her background in two videos posted on Sunday.

"I've seen chatter online questioning my identity and culture. This is something I take very seriously, and for those who are asking — I'll reiterate my story, as I've done many times before," she wrote along with a seven-minute video on Sunday. "I was born in Boston and grew up spending time with my family between Massachusetts and Spain. My parents and sibling live in Spain and I chose to live here, in the U.S.A."

Hilaria confirming that she was born in Boston is in contrast to what she has previously said and what is listed on her Creative Artists Agency profile, which says she was born in Mallorca, Spain — where her parents now reside. In addition — as many on social media have pointed out — Hilaria has claimed she moved to the U.S. from Spain at age 19 to attend New York University in an April appearance on the #MomTruths podcast.

And in a 2018 Hola! cover story interview, Hilaria was identified as Spanish while explaining why she was raising her kids to be bilingual.

Twitter users additionally cited an obituary for Hilaria's grandfather David L. Thomas, Sr., as proof that she is not from Spain. The obituary said that Thomas' family's presence in Vermont pre-dated the American Revolution and that frequent travels in Argentina, rather than Spain, led to the family's later proficiency in the Spanish language.

Hilaria has also frequently done media appearances using a Spanish accent while speaking, including one on Today where she appeared to forget the English word "cucumber."

Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories.

The yoga instructor — who is mom to Romeo Alejandro David, 2, Leonardo Ángel Charles, 4, Rafael Thomas, 5, Carmen Gabriela, 7, and Eduardo "Edu" Pao Lucas, 3 months — further claimed in her first video Sunday that her accent occasionally fluctuates based on whether she's been speaking Spanish or English more frequently around that time. She said she sometimes "mixes" them, calling it an insecurity of hers.

"We celebrate both cultures in our home — Alec and I are raising our children bilingual, just as I was raised," said Hilaria. "This is very important to me. I understand that my story is a little different, but it is mine, and I'm very proud of it."

The Mom Brain podcast co-host also confirmed that her name is Hillary, claiming that she used that name in America growing up because it was easier to say. She said that she decided to stick with Hilaria a "handful of years" before meeting Alec (the pair wed in 2012) so that she could "consolidate the two" names "because there were so many documents, so many different things."

"I identify more with Hilaria because that's what my family calls me," she said.

Hilaria went on to say she is proud of growing up with two cultures. "Yes I am a white girl," she said. "Let's be very clear that Europe has a lot of white people in there, and my family is white. Ethnically I'm a mix of many, many things; culturally, I grew up with the two cultures. It's really as simple as that."

"This is just who I am and my life story," Hilaria said at the end of the clip. "It might not fit into your cookie-cutter and might not fit into a label, but it's my weird mix of who I am."

Hours later on Sunday, Hilaria posted another video message on Instagram, further elaborating as allegations about her past continued to go viral online. She said, "I don't really understand why this is turning into such a big thing."

"At this point I'm starting to think I'm being attacked for who I am and no answer is the right answer," said Hilaria, who called the situation "strange" and "frustrating."

"I kinda just wanna say leave me alone. Leave me alone," she added. "I'm not doing anything wrong by being me. Maybe that doesn't look like somebody who you've met before, but, I mean, isn't that the beauty of diversity? ... This is not someone that's pretending to be something else, it's literally just you have two cultures."

Hilaria also said she feels like people are "trying to take my words and create a narrative because you're bored and at home, or something."

Alec and Hilaria Baldwin
Alec and Hilaria Baldwin
| Credit: Steven Ferdman/Getty

Many criticized Hilaria for impersonating a culture that is not her own, with Reveal reporter Aura Bogado tweeting, "The fact that @hilariabaldwin pretended to be from Spain with that ridiculous accent, while some of us have been denied opportunities for our actual accents, is disgusting. The fact that she pretended to be an immigrant, at a time of hatred, detention, and deportation, is sick."

Bogado added in another tweet, "Being an actual immigrant, having an actual accent, those are things that exist and are particular to certain people. Immigrants of color with accents find it even more challenging. It's beyond offensive that @hilariabaldwin pretended to be someone she's not."

Wrote another Twitter user in response to Bogado, "[Hilaria] deliberately used harmful tropes of Latina women to build her platform. She owes Latina women an apology."

Alec shared a video on Instagram on Sunday in defense of his wife, alleging that the claims about Hilaria are made-up Internet conspiracies without getting into any of the specifics. "You have to consider the source," he alleged. "We live in a world now where we're hidden behind the anonymity of social media, people feel that they can say anything."

He followed that up on Monday morning with a photo post of a quote that said, "Build someone up. Put their insecurities to sleep. Remind them they're worthy. Tell them they're incredible. Be a light in a too often dim world."

Hilaria's stepdaughter Ireland, 25, whom Alec shares with ex Kim Basinger, also defended her, addressing her followers on her Instagram Story Sunday night.

"It's so pathetic that anyone would want to play detective and dig that deep into someone's life that they don't know anything about, don't know how they were raised, don't know who they were raised by," Ireland said. "... And the last thing we really need to do is start s--- and gossip about something just so, so stupid."

"... She could be a malicious, terrible, horrible human who tears people down — but she isn't," she added. "Hilaria is a wonderful mother who takes great care of her kids and she takes great care of my dad and that's all that really matters to me."

Ahead of the allegations about Hilaria's ethnicity, she got into a back-and-forth with Amy Schumer on Instagram after the comedian reposted one of Hilaria's mother-son photos to make a joke about post-baby bodies.

On Sunday night, Schumer posted a photo of herself in sunglasses and a large hat, writing: "I get it. I went to Spain a couple times and loved it too," adding a cucumber emoji. She later deleted the post.

A rep for Hilaria did not immediately respond to PEOPLE's request for comment.