2003 SEL steering sways from acceleration

Hello All,

I recently purchased this vehicle about a week ago. In doing so I knew I would be investing some cash for repairs. This past week I so far replaced the right and left axles, purchased new Goodyear (factory size) tires all around including an alignment and had an inspection. There is improvement in the ride and the vehicle will stay straight during highway speed however I still have an issue with the steering briefly sways to the right from an acceleration. I am puzzled only because following the state inspection and the alignment done, if there is a steering issue how was it not picked up. I just need an idea what it may be.

Thanks in Advance.
Pachecos, New York