Sounds like your rear drums aren't adjusted correctly and/or your abs system isn't operating correctly.Be careful just swapping the fronts if you will have newer tires there! you always want better traction in the rears or you can spin out very easily!
I swapped the fronts temporarily like your plan and totally lost control on an on-ramp. I got very luck as no one was around and there was tons of road space.
New tires go on the rear.