The woman is holding a mug, and has sunglasses on the top of her head.
A woman is enjoying the outside weather, holding a cup of coffee, with her sunglasses on her head.
The woman could be holding a mug in any location, there is not way to imply that she is enjoying the outside weather.  Just because she is holding a mug does not mean she is holding a cup of coffee, because anything could be in the mug.
exists e2 e1 x1 x2 x3 x4 x5.(n_head(x5) & of(x5,x4) & n_female(x4) & n_top(x4) & n_woman(x1) & on(e2,x4) & of(x4,x5) & Theme(e2,x3) & Actor(e2,x1) & v_have(e2) & n_sunglass(x3) & Theme(e1,x2) & Actor(e1,x1) & v_hold(e1) & n_mug(x2))
exists e1 e2 s1 x1 x2 x3 x4 x5 x6.(n_head(x6) & of(x6,x2) & n_female(x2) & n_female(x2) & n_sunglass(x5) & of(x5,x2) & n_weather(x2) & a_outside(s1) & Theme(s1,x2) & for(e1,e2) & with(e2,x5) & on(x5,x6) & Theme(e2,x3) & Actor(e2,x1) & v_hold(e2) & of(x3,x4) & n_coffee(x4) & n_cup(x3) & Theme(e1,x2) & Actor(e1,x1) & v_enjoy(e1) & n_woman(x1))