This is bad compliance bushings, otherwise known as the lower control arm bushings. When you said you felt it worse while hitting the brakes makes me confident about this. Very common for these to fail on RX's. Have your trusted indy check this or take to the dealer for an estimate. This is an either semi difficult repair to do DIY, or a costly one to have done in a shop as it requires engine mounts to be loosened or removed so the engine can be jacked up just a little for removal. Typically I only use/advise OEM, but in this case try and source polyurethane bushings.