You didn’t say if your house is air conditioned but being in Dallas I expect you would have air conditioning. Since your exterior sheathing is so full of gaps the hot, humid air has no trouble getting into your wall cavity. When the hot, humid air hits the back of your cooler interior wall it will condense and get that area wet. With no insulation in the wall cavity it can now dry out. If you put insulation in the wall cavity it will absorb the water and stay well longer which is not a good situation. You must keep the hot, humid air out of your wall cavity. The only way to do that is to take your siding off. If you then put on a good air barrier and meticulously seal any exterior penetration and insulate from the exterior (foam board insulation, two or more layers, stagger the seams) you will keep the humid air out of wall cavity. The hot, humid air will come in contact with the foam board insulation but it will not be cold so it won’t condense. Also, use a rain screen under the siding to allow any moisture that gets behind the siding a chance to dry. You then don’t have to insulate in the wall cavities themselves.

I would not put the vapor barrier on the back of the outside sheathing from the inside. Your wall studs are then in the outside environment between two sheets of plastic. They will get cold from being in contact with your air conditioned wall. They will be a place for moisture to condense. If your wall studs get wet and don’t dry adequately you will have problems.

There’s no easy way around this. If you don’t do this right you will trap moisture in your wall cavity which will cause you problems… probably big problems.

Check out this presentation by Pat Huelman from the University of Minnesota on exterior insulation.