I think we will either take a taxi from the city centre to Anfield.It is only 15 minutes on one of the days.
I am thinking on the day of the parade, Chester to Lime Street and then from there to Mossley Hill, then walking it to Allerton Maze.
Have a couple of hours there, then, the train back to Lime Street and get the stop to James street at for 5 pm to see the end of the parade.