Frank Randall believed that it was his duty to stay in his marriage to Claire and help raise her unborn child. In spite of the certain knowledge that another man fathered the child, Frank also knew that he could not sire children himself. He may not have been sure, at first, how he would feel towards a child that wasn’t his, but once she was born, Frank was smitten with Brianna and loved her as his own.
Having searched for and discovered historical records about the man Claire named as Brianna’s biological father – and having potentially found out other as-yet-unknown truths about the dangers of being a time-traveler – Frank took certain steps toward preparing Brianna for a possible foray into the past, including teaching her to ride a horse and to shoot. Brianna was totally unaware of Frank’s motives until she found a letter from him addressed to her, years after his death. 
When Brianna meets Jamie in 1769, after a perilous journey of thousands of miles and two hundred years, she feels joy in the initial “honeymoon” phase of their relationship, but soon struggles to accommodate Jamie’s 18th-century attitude toward marriage and responsibility.
Brianna meets Roger in Scotland while on holiday with her mother, who had been acquainted with Roger’s late adoptive father. She flirts casually with him, and they kiss after a couple of weeks of performing historical research together.