Connect two grounding rods
Yes what you are doing is fine.  IV Grounding Methods ,  In the code 820.100  coaxial cable shall be grounded. 820-100  (A) through (D).   (A) (1) Grounding Conductor , shall  be insulated and shall be listed.  (2) Material copper solid or stranded.   (3) Size , shall not be smaller than #14 awg and shall not be required to be larger than #6 awg.   (4) Length ,run as short as practicable,not to exceed 20 feet in length.   EXCEPTION,  If you can not have that length,a ground rod may be used in dwellings.  Run the cable as straight as you can.  And protect the wire from physical damage,where you go into stucco sleeve wire in sch80 pvc conduit. And you may want to run conduit on inside wall of garage to electrode, or if that is the main panel to the ground lugs. all connected and bonded .