2 gear drop from which gear?

For me, problems shifting from large to small tooth count gears usually is not enough tension on the chain, likely just too long a chain, but maybe a dirty DR, weak spring perhaps. Or, the cable is not moving freely as the shifter relieves tension on it. Bad bend in cable housing somewhere, clamped a out front mount over the housing, cables cutting into the bottom bracket or the guide if it uses one.

However the one thing I had when I experience it is it takes an extra shift in the lever to get the shift change on the cassette that results in a two gear change. Or in other words, one click, no shift, one more click then a shift resulting in one or usually two gears smaller on the rear.

Might just be the cable tension screw or inline adjuster needs a half maybe a turn and a half.

Does the chain arrive at the largest sprocket and the smallest sprocket when the shifter is at it's limit in both directions? Or is there an extra click available at one end of the range?

If you don't know what all the pieces parts do that work together, then the bike shop will sort it out quicker. But if you have some mechanical inclination, then you might as well start gaining experience. Even if that includes looking over the shoulder of the guy at the bike shop first.......if they'll let you...... some do.