I made my share of mistakes with my first attempt. This may be more like what you want, with two distinct controls and correct syntax for ArcTan:

Manipulate[
 Row[{Plot[{Norm[p] Sin[2 \[Pi] t + ArcTan @@ p], 
     Norm[q] Sin[2 \[Pi] t + ArcTan @@ q]}, {t, 0, 1}, 
    PlotRange -> {{0, 1}, {-3, 3}}, PlotStyle -> {Red, Blue}, 
    ImageSize -> Medium],
   Spacer[20], 
   Graphics[{Locator[Dynamic@p, Background -> Red], 
     Locator[Dynamic@q, Background -> Blue]}, PlotRange -> 2, 
    Frame -> True]}],
 {{p, {1, 1}}, {-2, -2}, {2, 2}, ControlType -> None},
 {{q, -{1, 1}}, {-2, -2}, {2, 2}, ControlType -> None}]

For this particular example a 2D slider works quite well:

Manipulate[
 Plot[{Norm[p] Sin[2 \[Pi] t + ArcTan[p]], 
   Norm[p] Sin[2 \[Pi] t + ArcTan[p]]}, {t, 0, 1}, 
  PlotRange -> {{0, 1}, {-3, 3}}],
 {{p, {0, 0}}, {-2, -2}, {2, 2}}]

A variation:

Manipulate[
 Row[{Plot[{Norm[p] Sin[2 \[Pi] t + ArcTan[p]], 
     Norm[p] Sin[2 \[Pi] t + ArcTan[p]]}, {t, 0, 1}, 
    PlotRange -> {{0, 1}, {-3, 3}}],
   Graphics[Locator[Dynamic@p], PlotRange -> 2, Frame -> True]}],
 {{p, {0, 0}}, {-2, -2}, {2, 2}, ControlType -> None}]