Move the figure caption to the right?

It is much simpler to do that with the floatrow package, which defines a subfloatrow environment:

documentclass{article}
usepackage[showframe]{geometry}
usepackage{caption, subcaption}
usepackage{floatrow}
DeclareFloatSeparators{qqquad}{hskip 2.5em}
usepackage[demo]{graphicx}%

begin{document}

begin{figure}[htb]
floatsetup{subfloatrowsep=qqquad}
 ffigbox{%
 begin{subfloatrow}[3]
ffigbox[.25textwidth]{caption{image1}label{fig:1}}
 {includegraphics[width=linewidth]{Figures/sec_16-46_3.pdf}}
ffigbox[.25textwidth]{caption{image2}label{fig:2}}
 {includegraphics[width=linewidth]{Figures/sec_614-644_3.pdf}}
ffigbox[.25textwidth]{caption{image3}label{fig:3}}
{includegraphics[width=linewidth]{Figures/sec_852-882_3.pdf}}
end{subfloatrow}}%
{caption{Three images}}
end{figure}

end{document} 

[singlelinesheck=off] will stop the caption from being centered. Your best bet is to apply the hspace* to the entire subfigure (which is basically a minipage). I would replace [width=1.6linewidth] with [width=linewidth] and stop trying to overlap subfigures. If you aren't happy with the spacing, use hfill instead of hfil and adjust the subfigure widths.

Since floatrow is on my "packages to avoid" list, here is an alternative.

documentclass{article}
usepackage[showframe]{geometry}
usepackage{caption, subcaption}
usepackage[demo]{graphicx}%

captionsetup[subfigure]{singlelinecheck=off}

begin{document}

begin{figure}[htb]
begin{subfigure}{0.3textwidth}
  includegraphics[width=linewidth]{Figures/sec_16-46_3.pdf}
  caption{image1}
  label{fig:1}
end{subfigure}hfill
begin{subfigure}{0.3textwidth}
  includegraphics[width=linewidth]{Figures/sec_614-644_3.pdf}
  caption{image2}
  label{fig:2}
end{subfigure}hfill
begin{subfigure}{0.3textwidth}
  includegraphics[width=linewidth]{Figures/sec_852-882_3.pdf}
  caption{image3}
  label{fig:3}
end{subfigure}
end{figure}

end{document}