Keep Families Together and Enforce the Law Act This bill amends the Immigration and Nationality Act to authorize the Department of Homeland Security (DHS) to extend protective custody over alien children under age 18 who are accompanied by a parent and were apprehended at the border or are seeking admission to the United States at a port of entry. DHS must temporarily house an alien child in a DHS family residential center during the pendency of civil or criminal proceedings. DHS must (1) increase the number of available beds in family residential centers; and (2) secure the written permission of the governor of a state and the congressional delegation representing the state and the district in which any new immigration detention site, including any proposed new family residential center site, is proposed to be located prior to the construction or operation of such site. The Department of Justice must increase the number of immigration judge teams to conduct prioritized proceedings for accompanied alien children and families apprehended at the southwest border or who are seeking admission to the United States at a port of entry.