You dont need to go Dammam,

you can go this way:

Doha - Hofuf (No need to go the city) - Riyadh - sail al kabeer (You need to turn right before reaching Taif - here is your meeqat) - makkah

Makkah - Madina (straight road)

Madina - al Qaseem - Riyadh - HOfuf (again no need to enter city) - Doha

Make a stopover in riyadh (each way)

MAP http://www.malqatar.com/MAQ/media/Umrah%20Road%20Guide-Map-Mar09.pdf

Some information on the map is not correct