Re: Rotted Patio Door
That strip between the doors is called a T-astrugal, look at its shape, it will be self explanatory.
Yes, you can replace this strip, though you will probably have to go to a door and millwork supplier to get it, it is doubtful that any big box will carry such a thing.
As to fixing the door itself, it will depend on the severity of the damage, what you will have to do to repair it. If the faces of the door are ok, then you can carve or router out the damage and insert a repair piece cut to fit, glue and tack with some nails into the end of the door and clamp the faces to the block until the glue cures.
Install the new T-astrugal and mortice your handset/deadbolt and slide bolt hardware and you'll be good to go. This repair will probably take you 4 to 6 hours IF you have everything sitting there and waiting, longer if you've got to try to source materials once you've torn into the project.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!