Kalamaki --
You have, i think, two quite different issues: lens quality/speed, and lighting/flash control.
That Sigma is not a fast prime; f2.8 just like the best zooms and at most two stops faster than the kit zoom.
Aperture matters in flash photography since it determines how hard the flash has to work for a given ISO. Note that last clause: you should be able to get the same lighting balance with your kit, compared to the sigma wide open, by mulitplying the ISO by four (i.e. if the Sigma used ISO 800@f2.8, then the kit needed ISO 3200@f5.6).
As a general flash technique, the closer the ambient lighting is to needed exposure the smaller the problem of balancing illumination across the scene. On my FF dSLR i try to turn up the ISO to within a stop of exposure; if i can do that without blowing past ISO 6400 i easily get nice shots, particularly with wireless placement of multiple units.
But flash techniques -- which are not m4/3 strong suit in my experience -- are its own skill/discipline. The way you describe your problem, i think that that is where most of the issues are not your lenses.
Finally i note that Sigma sells a sweetheart of 19mm f2.8 prime (and 60mm for that matter) to complement your 30mm for under $200. That focal length / FOV is much more suited to most interior, flash, use.
Good luck. Experience and skills will improve your flash results. I do not think dropping $1200 on an f2.8 zoom would be a major step in that direction compared to the factors i mentioned.
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gary ray
Semi-professional in early 1970s; just a putzer since then. interests: historical sites, virginia, motorcycle racing. A nikon user more by habit than choice; still, nikon seems to work well for me.