There are many ways to order the points, especially if they form on concave polygon. For this case, the problem is easy. Say you have points $a,b,c,d$ in this order. Check the intersection between the two diagonals, $ac$ and $bd$, as segments, not infinite lines. That means that the intersection is between $a$ and $c$. If it is, you have a convex quadrilateral. If not, you have two options: it is either a concave quadrilateral, or the sides intersect, like in your case. Either way, if you swap any adjacent points (say the first two), you will get a quadrilateral. So $bacd$ in your case is OK. If you swap points on a concave quadrilateral you get a different concave quadrilateral.