Without seeing this first hand it sounds to me like your loader is working normally.
First of all, forget the idea that your boom or bucket should ,"remain ridged".
They are not ever ridged unless you welded them in a position and had steel wheels. Even then things flex or deflect some.
When you enter the soil or a pile with your bucket, you sometimes are exerting considerable forward roll pressure on your bucket. Then as the bucket begins to bite it is pulled down and you are now needing roll back presure to keep the bucket from diving deeper.
The compression and expansion of your hydraulic hoses on both sides of the cylinders between these two directions alone is enough to cause much of the drift.
Add to this boom flexure and tires; sounds normal to me.
This is called porpus-ing.
Normal.
With practice, you will get better and better at going with it and controlling bucket vector.
Forget "ridged". Its not there.
Have fun!