To back up a bit to before he becomes the Lord of Riverrun- Hoster Tully married Lady Minisa Whent of Harrenhal while his father ruled The Riverlands, before The War of the Ninepenny Kings. Together, Hoster and his wife Minisa had three children, though there were three more that did not survive past infancy. The timing isn't very clear as to if Catelyn was born before the death of her two brothers, though it seems unlikely she was. It is clear that Lady Minisa bore Hoster two sons that did not survive and therefore Hoster came to regard Catelyn as his heir. Another daughter followed Catelyn- Lysa, and finally a son- Edmure. Lady Minisa bore another son after Edmure, but Minisa did not survive that childbirth and the son died along with her. As reflected upon by Catelyn in her POV, Hoster Tully truly loved his wife and was deeply scarred and saddened by her death, missing her and just as sad decades later.
Rivermen, or Riverlanders are a mix of warriors, fisherfolk, and loyal common people. The noble River Lords are known to be quarrelsome with one another; an extreme example of this would be Houses Bracken and Blackwood whose rivalry and aggressive relationship goes back to The Age of Heroes. The location of The Riverlands and the lack of natural boundaries amongst the lands claimed by the noble houses are major reasons for the nature of these noble houses.