It sounds as though the front suspension has one or more worn parts.

Applying the brakes causes a shift in suspension parts that is aggravated by one or more of the following:  An wheel out-of-balance condition, out-of-alignment condition, or worn parts including tie rod(s), ball joint(s), and/or control arm.

This should be checked by a mechanic you trust and has experience in examining front end suspensions and replacing only the necessary parts and doing only the needed repairs.

Mark L., OK