As a workaround, I defined the following function Aaargh:

ee:=[e1,e2,e3];
dimee:=3;
Aaargh:=X->add(GetComponents(X,ee)[i]*ee[i],i=1..dimee);

The function Aaargh extracts the coefficients from _DG(...) and transforms them into scalar coeffiencets in front of the vectors of the basis ee. For instance,      _DG([["vector", LA, []], [[[3], -4]]])     becomes       -4*_DG([["vector", LA, []], [[[3], 1]]])       , etc...

Then I use the function Aaargh every time I think there may be the issue above. For instance, one could redefine the Lie brackets:

myLieBracket:=(X,Y)->Aaargh(LieBracket(X,Y));

All the issues above disappear in this way.