There was no time in the battle of Cross Keys that Jackson’s contingent was under threat by Fremont.
As to the battle of Port Republic, Jackson’s victory there was total after initial surprise by federals and hard fighting until the federal artillery position was turned at the coaling.
As a matter of personal information, I had occasion many years ago as a child to visit Conrad’s store (now Elkton) the place where the rout of the federals finally stopped. There a brick building was pointed out to me by my relative who stated that the building served as a Yankee hospital after that battle and that a pile of limbs grew on the ground outside the only window on the second floor facing east from which the amputated limbs were thrown.
The victories by Jackson at Cross Keys and Port Republic were complete and serve as a triumphant Conclusion to Jackson’s historic Valley campaign of 1862.
Yes, Fremont was just too slow to do much to Jackson, but, Shields got close to taking Port Republic.
By the time the shooting stopped, Fremont did have troops overlooking the river, but, he was just sooooo slow.