Any immigration authority has this basic problem when illegal aliens arrive with children. 
1. You can just decide to let them all stay.  A slap in the face for those who apply legally and wait for years. 
2. Send them all back over the border. They try again the following day until they don’t get caught. 
3. Put the entire family in prison.  Surely cruel and illegal to lock up children with their parents. 
4. Put the parents in prison and take the children into care. 

Your choice but only 4 makes sense. 

No compensation should be paid to those who entered the country illegally except under the most extreme circumstances.