i have a 2000 ford explorer sport and when i drive it at all it will shake and wobble back and forth. Not at a specific time, just when i drive it at all. I think it might have something to do with the tires maybe.
The list of possible causes is really long and could include tires. The list also includes a lot of things that can be really dangerous. You really need to just take it to a local and reputable mechanic, preferably a good front/end & tire shop to have them drive it and give everything a once over.