Jenna Bush Hager Reveals How George and Laura Bush Embarrass Their Grandkids When They Come to Town (Exclusive)

Even famous grandparents embarrass their grandchildren.

Jenna Bush Hager tells PEOPLE in this week's cover story that daughter Mila, 11, is at the age where she's beginning to grasp exactly what a visit from her grandparents, former President George W. Bush and First Lady Laura Bush, entails.

"My mom came to visit a couple of weeks ago, and we were driving around, we went to dinner, and Mila looked at me and she's like, 'Are you humiliated?'" recalls Jenna. "I'm like, 'What? Why would I be humiliated?' And it's because of the Secret Service entourage!"

Jenna's twin sister Barbara Bush empathizes with her niece, agreeing that the attention can be a lot.

"She does not like that, which is another reason she's sort of like you," adds Jenna.

The Jenna & Friends host tells PEOPLE that she later asked Mila if she'd want her grandmother to tag along for "Bring Your Special Person to School Day."

Mila wasn't so thrilled with the idea.

"She's like, 'Sorry Grammy, but you can't do that. You can't do that.' Because she just can't imagine!" Jenna explains.

For more of Jenna and Barbara's exclusive interview, pick up this week's issue of PEOPLE on newsstands Friday.

Jenna and Barbara recently authored a new children's book, I Loved You First, which Jenna says is all about trying to "see the world through your kids' eyes."

The minute she put herself in Mila's shoes, Jenna realized her daughter's feelings made perfect sense.

"She's also of that age. She's in middle school, when you start to internalize what it feels like to be in your position. So she was like, 'This is embarrassing.' And I was like, 'No, Mila, I'm not embarrassed now!' But then I felt bad that I said that because [Barbara and I] would have totally been embarrassed in seventh grade," she admits.

For all of the conspicuousness that comes along with a Secret Service entourage, however, Mila is still able to have a little bit of her own good-natured fun.

"We're the car with the Secret Service and Hal's like, 'Are those the Secrets Service?' I'm like, 'Yeah,' and Mila and Poppy are like 'You better act great, or they're going to arrest you!' And Hal was like, 'But I didn't do anything!' I know, poor Hal. We get why he is who he is," jokes Jenna.

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Today with Jenna & Friends airs weekdays at 10 a.m. ET on NBC.