IMO, if there are six games a week on average and two are vs. LHP here’s how I’d address the issue if everyone is healthy.
Versus RHP:
1B: Abreu (3/4) | Sheets (1/4)
LF: Jimenez (3/4) | Vaughn (1/4)
RF: Pollock (3/4) | Vaughn (1/4)
DH: Sheets (1/4) | Vaughn (1/4) | Grandal (1/4) | Jimenez (1/4)
CA: Grandal (2/4) | McGuire (2/4)
Versus LHP:
1B: Abreu (2/2)
LF: Jimenez (1/2) | Pollock (1/2)
RF: Pollock (1/2) | Engel (1/2)
DH: Vaughn (2/2)
CA: Grandal (2/2)
This allows the core starters (including Vaughn) to play five out of every six games. Sheets gets two starts a week against tough RHP, McGuire starts two games against RHP (where he is solid), and Engel gets a token start plus late game duties. If someone goes down, then Sheets’ playing time increases substantially. Until then he should be a role player whose playing time reflects that.