New to you vehicle, no paperwork... YIKES! People rarely sell running, inspected, and 100% operational vehicles, buyer beware. We'll get you through this, get your wallet out.
It has been my GENERAL AUTOMOTIVE EXPERIENCE, that shuddering of the nature you describe is about SUSPENSION issues, and possibly brakes and wheel bearings.
Firstly, I'd be looking at the shock tower bushings, broken springs, tie rod ends, ball joints, and control arm bushings. Dip is related to shocks and springs. Wobble is tie rod ends, steering dampeners, warped rotors, bad shocks. Pulling is control arm bushings, ball joints, tie rod ends, and shock tower bushings.
Yea, brakes play into this scenario, but the dipping and INTENSE shuddering indicate the suspension is faulty, IMHO. It sounds to me like someone hit a curb or huge pothole and actually broke some suspension bits.
Pop the hood, place your hand on the shock tower, and put all your weight on the vehicle, making it bounce up and down. Feel for movement and noise on that shock tower(and other places!). Do this on both sides for comparison. Have an assistant(I prefer attractive 5'7" blondes with assets, but a caveman will suffice) turn the steering wheel while you hold your hand on the tower, again both sides.
Get the vehicle off the ground. Yank on both wheels in all directions, looking for any "play" and noise when you spin that wheel. Have an assistant turn the steering wheel lock to lock and "feel" for movement and noises. Put a grip on the tie rod ends and see if you get movement from either side, especially the "bad" side. Inspect the bushings, ALL of the bushings in that area, both sides, of course. Look for cracks and out of center alignments in the rubber bits.
Ball joints are a bit trickier, since you need to feel for a clicking or movement when the weight of the vehicle is applied on and off those joints. A long breaker bar can be wedged around the control arms and ball joints by someone familiar with such testing, probably not a recommended DIY task.
What does your tire wear indicate? If this has been going on for some time(which I suspect it has), there should be uneven wear on the "bad" tire.
Bottom line: You might be better off getting professional help on this diagnosis, and I doubt it will be an inexpensive repair. Budget $100-600?
All that being said, I would then also explore the brake and wheel bearing possibilities.
After you perform the above tests, get back in here and Tell us what you found. We'll then attack the brakes and bearings inspection, which is a somewhat simple DIY repair by comparison to suspension issues.
FWIW, the blonde will surely be impressed with your expertise during this diagnosis(she owes you a reward!), the caveman, not so much.