Dual citizenship is a tough one. See Afroyim v. Rusk, 1967
Basically, the SCOTUS says you have a right to be a citizen of more than one country. So, until that's overturned, any EO or law to the contrary is a no-go as unconstitutional.
Well, you obviously have strong feelings about this, but the SCOTUS really doesn't give a shit. They said that US citizens cannot have their citizenship taken away involuntarily.
If you want to deal with the immigration problem, get a ruling on the 14th amendment that is retroactive. No anchor babies. Now all those who got citizenship because of some kid are no longer citizens because they actually never met the criteria.
They have to go back
While you're at it, you can also see about getting Afroyim v Rusk overturned.