2006 Honda Odyssey Question: Steering wheel shakes & no tire traction in rain

The wheel never shook (side to side vibration) and I never had a problem with spinning tires or traction in the rain, before I replaced the no flat tires and wheels with tires that anyone can change. Honda recommended a tire shop to change the wheels and I put on new tires. I noticed at high speed (65 MPH) vibration in the steering wheel and returned to the tire store. They aligned and balanced the tires. Steering wheel continued to vibrate and I still had poor traction in the rain so I took the van to Honda. They said it was a brake problem. Vibration continued even after Honda repair as did poor traction in the rain so I bought Michelin tires and had tires balance and aligned. Still vibration continues only at high speed and since it hasn't rained I don't know about the traction. I am now thinking of buying a new van. I would like to keep my Odyssey and hope you can come up with an answer.