The best way to deal with illegal immigration is to enforce laws against employing illegal aliens with very heavy fines to employers. This should be applied to anyone employing an illegal, large corporations and homeowners employing gardeners.
If illegals can’t find employment then they will not stay.
If an apparently pregnant woman arrives at any border crossing, including airports, their citizenship must be immediately confirmed. If not an American citizen or legally married to an American citizen then entry must be denied.