Bacharach Family

My Family is related to 2 separate ( ? ) Bacharach families.
Bacharach from Prague
One is that of Rabbi Yair Chaiim Bacharach to who we are related via the Heymann family to Gerber then Oppenheimer Family from Heidelberg (the family of his wife).

Bacharach Family from Kassel, Hessen
The family is that of my Grand Mother from Kassel, Bertie Babette Bacharach and her father Solly and Grandfather Baruch Bacharach.
The Bacharach Family first appears in Hessen in the Frankfurt am Main from 1391

My GrandMother's Bacharach Family

Tradition has it that all Bacharach families came from the town of Bacharach on the Rhine river district of Coblenz.
A name frequent among German Jews. From the twelfth, or at any rate from the fifteenth century, the name Bacharach, in various spellings—as Bacharach, Bachrach, Bachrich, etc.—is found among the Ashkenazim in all parts of Europe. Although all individuals bearing the name hardly form one family, the name merely indicates that the family either derived its origin from the city Bacharach in Rhenish Prussia, or that one of its ancestors was at one time a resident of that place

Bacharach was passed through by the Crusaders in the 13th Century, who massacred the Jews they found there. On April 19, 1283, twenty-six Jews were murdered there, among them the boy Hezekiah, whose father, Jacob, had been killed at Lorch in 1276. In 1287 the Bacharach Jews were subjected to persecutions caused by the murder of Werner, who was made a martyr of the Church. This persecution has been described by Heine in his "Rabbi von Bacharach." In 1337 the mob, under the leadership of Armleder , attacked the Jews; and in 1349, at the time of the Black Death, many of them were slain. From 1365 to 1370 the counts palatine took a number of foreign Jews under their protection and permitted them to settle at Bacharach; and in 1510 the permission was renewed. In 1722 only two Jewish families lived there, while by 1901 there were 46 Jewish residents.
Of the Jewish scholars of Bacharach, records of the second Crusade (1146) mention Alexander ben Moses, Mar Abraham ben Samuel, and Mar Kalonymus bar Mordecai. These, with their households, sought refuge in the castle of Stahleck, where they were killed. Their remains were brought to Mayence and interred there.