First of all, you are going to need to modify the core: It needs a gap. In a perfect transformer, the lines of magnetic force would be entirely confined to the core.

http://en.wikipedia.org/wiki/File:Transformer3d_col3.svg

There would be no place where any other object could be affected by the magnetic field. Somehow you need to break the "magnetic circuit." With most transformers, the core is made in two pieces that were assembled together after a spool containing the windings was put into place. Maybe you can break it back into two pieces. If it’s a toroidal transformer though, then you might as well start from scratch.

http://en.wikipedia.org/wiki/Magnetic_core
http://en.wikipedia.org/wiki/Magnetic_circuit

As far as using both windings goes, it is not as easy as you might think, and you may not reap as much benefit as you might think. You may not reap any benefit because, in a well-designed transformer, the primary alone will be capable of driving the core close to saturation. The combined effect of driving both coils is not likely to substantially increase the magnetization of the core.

http://en.wikipedia.org/wiki/Saturation_%28magnetic%29

The other problem is related to the power supply. Since the original purpose of the transformer was to "step up" a given voltage, the voltage and current limits of the two coils must be very different. You won’t get the strongest possible field if you wire them in series, because the amount of current in the series circuit will be limited by the capacity of the secondary winding. Likewise, you won’t get the strongest possible field if you wire them in parallel, because voltage needed to drive the maximum allowed secondary current will be too great for the primary. You would have to supply each coil from an independent power supply to get the best performance, but like I said, that’s not really relevant if one coil alone is able to saturate the core.

I would just use the primary, and forget that the secondary is there.