There will be two kinds of birth certificate; one for children born to citizens, legal residents, and those who have one parent who is a citizen/legal resident. A second would be for children born to non-citizens, and those who can't prove they are here legally.
Since the several states are the ones who decide who is a citizen of their state, and issue birth certificates for those born there, it isn't an issue the Federal Government can get involved in. Naturalization of non-citizens (they get Federal papers issued, not state certificates) and immigration of same is.
The idea is to discourage those illegals who come here to have children so that they can stay. It will go to court, of course. But that is the plan.
“but we can stop it from happening again.”
Sure, but this would only ever take place after the fact. By the time this is relevant, it’s already too late. You are conceding that you cannot stop it by preventing the entry of illegal immigrants into America.
“There will be two kinds of birth certificate”
“Since the several states are the ones who decide who is a citizen of their state”
And two Americas. One slave, and one free. ‘A house divided amongst itself shall not stand’.