Front wheel riders side noise

The shaking should not happen. Has this just started since they replaced the bearings?

As far as the 4wd computer, there isn't one just for the 4wd. There is an actuator on the transfer case that engages the 4wd. Is that what you are refering to?

Raise and support vehicle. Remove wheel assembly. Remove and discard hub nut and washer. Remove brake caliper and brake caliper bracket assembly. Remove brake rotor retaining screw (if equipped), and remove brake rotor. Remove 3 brake rotor shield retaining bolts, and remove brake rotor shield. Remove ABS sensor retaining bolt, and disconnect sensor.
Remove 3 wheel hub retaining bolts, and remove wheel hub and bearing assembly. DO NOT over-extend CV joint. Slide hub and bearing assembly off of CV axle shaft splines. CV joint should slip fit into wheel hub and bearing assembly and should not require puller to remove. Remove steering knuckle grease seal. Inspect steering knuckle grease seal, hub and bearing assembly for excessive wear and damage. Replace components as necessary.
Installation
Using Bearing Cup Replacer (T80T-4000-P), Knuckle Seal Replacer (T96T-1175-A) and Threaded Drawbar (T77F-1176-A), install seal until it seats against steering knuckle. Connect ABS sensor to wheel hub and position wheel hub assembly onto axle shaft and knuckle. Install hub retaining bolts and tighten to specification. See TORQUE SPECIFICATIONS. Install NEW washer and hub nut, and tighten to specification.
Install ABS sensor bolt and tighten to specification. Install brake rotor shield and tighten bolts to specification. Install rotor. Install brake caliper and brake caliper bracket assembly. Tighten bolts to specification. Install wheel and lower vehicle. Before driving vehicle, pump brake pedal several times to restore normal pedal position.

4x4 has no cotter pin
check the fig. Check out the diagrams (Below). Please let us know if you need anything else to get the problem fixed.

This is a fairly common problem with this model. Mine does the same thing! And I have 30 years of experience as a Ford technician!

I have found that if you follow the shop manual procedure for tightening the bearings, and they are using the proper lube, they tend to stay tight longer. However, this seems to be just one of those things that requires periodic maintenance.

Could be, the way to check other than pulling the wheel off is jack the explorer front end off the ground, wiggle the tire back and forth to see if there is any play. With the wheel jacked up and in neutral turn the wheel by hand while you are gentle touching the spring. You will be able to feel it through the spring if the bearing is going bad. Take a little practice but it works.