> So if anyone can tell me what I'm doing wrong below, I'll be grateful.

Two mistakes...

> #macro vec2rot(V, A)
>      #local _X_ = -V.u*cos(A)*sin(A) - V.v*cos(A)*sin(A);
>      #local _Y_ = V.u*sin(A)*cos(A) + V.v*sin(A)*cos(A);
>      #local RESULT = <_X_,_Y_>;
>      RESULT
> #end

This is wrong, should be:

#macro vec2rot(V, A)
     #local _X_ = V.u*cos(A) - V.v*sin(A);
     #local _Y_ = V.u*sin(A) + V.v*cos(A);
     #local RESULT = <_X_,_Y_>;
     RESULT
#end

You seem to have made it too complicated, it's just a 2D rotation:

https://en.wikipedia.org/wiki/Rotation_matrix#In_two_dimensions

> #local np1 = (len/sqrt(7))*vec2rot( vT,asin(sqrt(3)/(2*sqrt(7))));
> #local np2 = (len/sqrt(7))*vec2rot( vT,-asin(sqrt(3)/(2*sqrt(7))));

These are wrong, should be:

#local np1 = p0 + len/sqrt(7)*vec2rot( vT,asin(sqrt(3)/(2*sqrt(7))));
#local np2 = p1 - len/sqrt(7)*vec2rot( vT,asin(sqrt(3)/(2*sqrt(7))));

np1 is at p0 plus the distance len/sqrt(7) times your new direction.

np2 is at p1 *minus* the distance len/sqrt(7) times the new direction.

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