A man is standing behind a cart, outside, with two children inside and one child outside.
A man is near a cart with his kids inside
Standing behind a cart implies being near the cart.  If a man is spending time with some children, they're probably his children.  " Kids " is a synonym for "children".
exists e1 s1 x1 x2 x3 x4 x5.(with(e1,x3) & inside(x3,x4) & n_outside(x4) & of(x4,x5) & n_child(x5) & card_eq_1(x4) & n_child(x3) & card_eq_2(x3) & a_outside(s1) & Manner(e1,s1) & behind(e1,x2) & n_cart(x2) & Actor(e1,x1) & v_stand(e1) & n_man(x1))
exists p1 x1 x3.(exists x2.(near(x1,x2) & with(x2,x3) & r_inside(x3) & n_cart(x2)) & n_kid(x3) & of(x3,x1) & n_male(x1) & n_man(x1))