what is the net effect of nodal and apsidal lunar precession? In apsidal lunar precession, the moon's elliptic major axis precesses eastward and completes one revolution eastward in 8.85 years.  Because the orbit is inclined relative to the ecliptic, basic geometry dictates that the ascending and descending nodes must also rotate about the ecliptic at the same rate (all else constant.)  But then there's nodal precession, rotating the nodes in the opposite (west) direction, one revolution every 18.6 years.  So what is the net effect of these two precessions on the positions of the nodes? Subtract the two?
(Hope I’m not too late, two and a half years later… Just saw this post now—and I wasn’t a member of Astronomy SE back then…)
The short answer is no. These two effects don’t occur in the same plane. Imagine the lunar orbit as an elongated ellipse—much more elongated than it is in real life. Imagine the Earth as one of the foci, closer to one tip than to the other. Imagine the plane of the ecliptic as, if you wish, parallel to your floor or your desk. Now, the Moon’s orbit is tilted—by a small amount, about 5.14°—to the ecliptic (NOT to the Earth’s equatorial plane, like other planetary satellites, but that’s a different story). So imagine your first ellipse tilted with respect to your floor or desk.
The first movement, the precession of the perigee, makes it so the ellipse pivots in is own plane around the Earth. So its plane doesn’t change at that point.
The nodal precession, though, changes the orientation of the plane. The movement is still around the Earth, but parallel to the plane of the floor or the desk.
The closest everyday parallel I can find is if you own a ventilator (fan) that pivots on itself to aerate in different directions. The movement of the fan blades would represent the apsidal precession (the first you mention), while the swiveling of the fan head left and right would represent the nodal precession.
Hope this helps!