*** he had to do was push his army to its limit to catch up to and pass the ANV and place the AoP between the confederates and the Potomac, forcing Lee to attack against Meade's prepared defenses, even If he had to do it from the South Bank of that river(Meade had bridges across the river and Lee did not)."
No it was not and the mere assumption is pure silliness. Read the book. Moving an Army. any ARMY, in 1863 during the best of conditions was difficult at best. The ANV under Robert E. Lee had just been defeated but at a very high price in blood and supplies. The battlefield was cluttered with the detritus of war. Wounded by the thousands needed treatment. Soldiers and commanders had not slept in days and some had not eaten or had water. READ THE BOOK!!!
I agree, there was no way the AOP was going to catch up and pass the ANV. The ANV had a head start and still had the ability to force actions at the rear of its march (check out the Battle of Monterey Pass sometime).
The AOP was a bigger army than the ANV with a lot more wagons, etc. to move. Just to give you some idea, I used to work at Gettysburg and at one July 2 commemoration event we had to move 300 tourists from the parking area near the top of Big Round Top down to Devil's Den, less than half a mile down a path. Took us 45 minutes and we were only moving people.
The AOP had a lot of wounded to care for, and not all were there own. The ANV left a lot of wounded behind for the AOP to handle. The ANV also left a lot of broken wagons and the like along the road during the retreat for the AOP to have to deal with.
The ANV was taking the shortest routes to the Potomac. Where exactly was the AOP going to pass them? The AOP took other routes that should have been easier in the rain but were longer.