Hello muha,
There are too many variables at play to give you a simple answer. This is complicated by the fact that the original equipment manufacturer's design or quality processes were not adequate for the service. You have alluded to this fact by suggesting that welding over the old weld is likely not a sustainable solution. I agree with that observation and suggest that you are on the right track by trying to modify the construction at the joint. I cannot tell you exactly how to do that. Instead I will offer you some steps to determine the correct repair method.
First, contact the manufacturer and see if they will share some technical information. You need to figure out how to weld the parent material to the repair without compromise to either material. To do so you will need to know the tubing chemistry and dimensions. That is normally provided by stating a material class (ASTM or some other standard) and a statement of outside diameter and wall thickness. Next you should ask them for a recommendation for a weld procedure. Finally, you should know if the joint was stress relieved (PWHT = Post Weld Heat Treatment). With this information in hand you can visit your welder and select the materials and welding method to provide an appropriate repair.
That said I can suggest a couple of things to consider for the repair. Once the old weld is ground out (you don't put a new bandage over an old bandage) then the hole will be bigger than the cross bar. So some method of patching the hole is necessary. A reinforcing pad rolled to suit the outside diameter of the main tube could be fashioned with a short length of tube attached that will form a socket to receive the cross bar. The fit of all the parts should be close tolerance so that they are tight before welding. The pad is then welded to the main bar and the cross bar is welded into the socket. Alternatively I would think about replacing the section of the main tube with one of a larger diameter. I would make it long enough to capture at least both cross bars and maybe longer if some other members might impart a torsion on the main tube. The front and back frame parts could be cut and inserted into the new main frame tube segments and socket welded in place. In all cases the final fit up must be true and square to avoid introducing racking or twisting under load. Don't forget to prime and paint the raw steel to avoid rusting.
Or if the new frames are only $150 then buy two and throw them away each time they fail. Or maybe upgrade to a higher quality product? That seems easier to me.