In most of these cases of immigrants from Central America, the conditions in their homeland pose more risk than being dragged through Mexico and seeking asylum in the USA. Both staying in their homeland and traveling a few thousand miles under less than ideal conditions pose dangers. However, remaining in a violent, lawless country is the more dangerous of the two options. They will keep coming as long as where they're going is providing a glimmer of hope.
Nobody's children deserve to be harassed. It doesn't matter whether or not they are a politician's children or the children of immigrants. All children deserve to be protected. That should be the bottom line.
Many would also say, that true asylum seekers could go to other closer countries, or CA's could stay in MX (which is typical international asylum law). It's also pretty evident that some bring their kids knowing their chances with a kid are better... Perfect example is the child on the Time cover. The mother left her husband and 3 other children without telling them. She wanted to join other family here and had a job lined up per the husband. She was not fleeing persecution. She had also been deported before when she attempted to come by herself.
Sorry, but I'm very skeptical of most "asylum" claims. The system is being manipulated, and the economic asylum seekers make it very hard to help the actual persecuted asylum seekers. By playing the CA card, you're pretty much saying anyone from Guatemala, Honduras, or El Salvado should have an automatic free pass into the US.
Compare Syria to the CA Triangle. Syria is war torn while the CA Triangle has gangs. Europe is turning away boats from Syria, yet we're horrible for not having an open border for CA.