The submitted research paper describes the fundamental findings in terms of multiaxial fatigue of the basic material EN AW6063 and its welds for implementation in the frame design of an unconventional vehicle. It also includes a briefly-presented conceptual design of a technical solution for optimizing the functionality of a steering mechanism in a patented unconventional vehicle, designed by the authors to increase the cornering stability of a vehicle–tricycle. The most important part of this article is the description of the ongoing research and the results of multiaxial fatigue (bending–torsion combination) of the structural material for the construction of the vehicle frame. The research in this area is important due to the increased load on the frame during operation caused by the unconventional steering mechanism. The measured and constructed Manson–Coffin curves indicate that the use of material EN AW6063 is possible for this vehicle in terms of multiaxial stress. This also applies to the material affected by the technology in the frame production (TIG welding). A higher fatigue of the basic material was observed at a 90° phase shift. The difference between the 0° and 90° phases practically makes up approximately 10 to 15% of the difference in the cycle numbers with the same deformation amplitude. At the same time, the measured results show that the phase shift between loads will not play such an important role in welded joints of aluminum alloy EN AW6063. When comparing the dependences with a constant deformation amplitude in bending and in torsion, it can be said that the bending stress will react more to even a small change in the deformation amplitude. Bending has been proven to be the more dominant component of the total deformation amplitude in multiaxial tests. In terms of low-cycle multiaxial fatigue (up to 5 × 105 cycles), a higher fatigue of the basic material is found in comparison with the weld. At lower deformation amplitudes, a higher fatigue of the welded material is detected.