The issue of unauthorized immigration should be addressed by improving the conditions of other countries. "thousands of Mexicans, some with their families, cross without authorization into the united states each year looking for work". Having more jobs in the places these immigrants homes/countries they would stop them from coming over and breaking the law. America would have less problems with immigrants. Immigrants would have a job and would be able to support their families.
The problem of the fugitive aliens should be handled by putting the criminal in jail after trail. "so most are simply detained and then bus them back across the border." often do they try again after a couple of days.
If immigrants were to be left in jail for a while maybe then they will give up. Can happen when breaking the law. But it can also stop many of them immigrants from coming back.
Children who have been brought into the country should be granted citizenship. "their children attend public schools" a lot of them try hard because since they see that they have a huge opportunities here. They can be really smart and try more then actual born citizens. Giving immigrants kids citizenships would be a good thing, it can be helpful to them and their families.