Q: how were political machines a danger to economic and political freedom in the late 19th century?

Political machine were political groups that emerged in the late 19th Century that usually managed immigrants and set them up, if immigrants would vote for them in return political machines will provide food, housing and jobs for the immigrants. A Political group was commanded by a boss that had enough votes to maintain political and administrative control of a city, county or state.

The political machines were detracting the basic principles of economy and political freedom in the US by people doing voting and party work to get others to vote for them like some kind of slavery, owning people once consent was given by the weak one. From the economical point of view these political machines were trying to concentrate the economy on their side by using their political status to assigned government contracts and jobs to those that did favors to them and this way creating a big spiral of corruption and putting in danger the political an economical policies of US.  

your mothers brothers brother in law would be your father.