I need help animating a kite :)

Hi guys, I´ve been trying to figure out how to animate a kite. I want it to be a cloth simulation using wind. I´ve set the following vertex group for the "shape" in the cloth settings, because I want this kite to have this T/ cross structure.  however, as the cross is part of the "shape" the kite stays still in the same spot like this:

What I want is that the whole structure (cross) moves all around affected by the wind, on the other hand, as it can be shown in the gif, I want the kite moves exactly like that maintaining its shape. 

I´ve tried something different by selecting a vertex group, which only includes the last vertex of the cord, and removing the T/cross section,  the kite moves as I want,


but it doesn´t maintain its cross structure and gets completely deformed. What should I do for this kite to keep the T shape and at the same time be able to move based on the wind force field?
I have both parts of the kite either joined in one single object or separate like this:

Which would work better, joined or separated? If separated, what can I do for the cloth simulation of the kite to be affected by the second object, the cross, and attach them to each other to move like a single object, while maintaining the rigidity of the cross-section and the clothing properties of the kite?

Thanks in advance!