As you have it now, it's just a simple fifth relationship. You're in the key of C, and you have iii7 moving to vi.
In order to have a secondary dominant (also called an "applied chord"), you want to temporarily use the leading tone of the chord you're moving to. You're moving to A (vi), so you want to actually use this key's leading tone (G♯) in that E chord.
Therefore, your Em7 chord will become E7 (E G♯ B D), and that chromatic addition of G♯ will add in the color I think you're looking for. You can experiment whether you want the G♯ to begin right on the downbeat of that measure (what I would recommend) or on the second half.
In making this Em7 an E7, we can now better analyze it as V7/vi. In this way, we show precisely how this chord is functioning: as a secondary dominant of vi. This label is much more informative than just calling it something like III7.
(And technically speaking, we tend to resolve chordal sevenths down by step. This means that D, the chordal seventh above E, will want to resolve down to C in the next chord. You do this in the middle staff, but it looks like the D in your top staff resolves up.)
As for the chord sounding "muddy," it may because of how you've voiced it. Notice that you have two Bs, two Ds, and only one G(♯) and one E. Typically you'll want to double the root (E) before you double anything else. Even changing the D in the middle staff to an E might make a big difference.