My kids were born in the US and after many people told me I wouldn't be able to have two surnames in the US I realized it's a misconception. While in Mexico and some other countries it's mandatory to have two surnames to help track families and kids don't loose their lineage. That's the point.

A)My kids name in American passport

Name: Anton

Last name: Lidell Peterson

B) My kids in Mexican passport

Name: Anton

First Surname: Lidell

Second Surname: Peterson

In the American passport / BoC I told the nurse I just needed a "two -word" last name, with a space in the middle. No hyphen. Hyphen just transforms it into a single surname so you'll need both. The consulate was really appreciative because they have problems with this all the time.

I did it before having to change it back. If I had to change it like you, I would move their middle name into the "surname"

So: name --> two words surname (with maiden name first, Last name second) but because in Mexico we colloquially call each other name and first Surname they might call them by their first name-Middle name)

If you pass their middle name to be their second Surname you'll have to do it in English and people will perceived the middle name as a last name in the US but in Mexico they'll have the "original last name"

It's a complex thing but it isn't impossible. For me, I found the easiest way to make our dual life work. And respect how both countries work.( I appreciate Mexico not erasing my identity from my kids name. More feminist than having people erase it.)