Rectangular Collision Resolution behaving incorrectly on corners

Question

I'm currently writing a simple game engine and encountered an error while trying to resolve rectangular collisions. When an object moves diagonally and collides with a solid object I only correct it in the axis that would require less translation to resolve the collision. The problem with this is that when a diagonally moving object travels "over" a corner the smaller axis flips to the opposite axis before the two objects stop colliding and the non-solid object "teleports" to fix itself.

Here's a piece of the collision resolution method (c++):

/*
    0: UP
    1: UP RIGHT
    2: RIGHT
    3: DOWN RIGHT
    4: DOWN
    5: DOWN LEFT
    6: LEFT
    7: UP LEFT
*/
switch(lastDir){
    case 0:
    {
        rect.y = (other->rect.y+other->rect.height)+fixed(0.0078125); 
        //0.007 is padding amount, fixed is fixed point number class due to hardware constraints, rect is rectangle with x, y, width, height
        break;
    }
                        
    case 1:
    {
        fPoint l1(rect.x, rect.y); //fPoint is Point using fixed
        fPoint r1(rect.x+rect.width, rect.y+rect.height);
        fPoint l2(other->rect.x, other->rect.y);
        fPoint r2(other->rect.x+other->rect.width, other->rect.y+other->rect.height);
        fixed distX = abs(min(r1.x, r2.x)- max(l1.x, l2.x));
        fixed distY = abs(min(r1.y, r2.y) - max(l1.y, l2.y));
                        
        if(distX > distY){
            //if y is shorter correct y
            rect.y = (other->rect.y-rect.height)-fixed(0.0078125);
        }
        else if(distY > distX){
            //if x is shorter correct x
            rect.x = (other->rect.x-rect.width)-fixed(0.0078125);
        }
        break;
    }
                    
    case 2:
    {
            rect.x = (other->rect.x-rect.width)-fixed(0.0078125);
            break;
    }
//continues for directions 3-7
}

Answer 1

Not exactly a solution to this problem, but I solved my problem by changing to a different resolution method. In my new one we check to see if our previous tick was within the width or height range of the solid object and then continuously correct based on that.