Stangs are especially notorious for understeer (front end loses control) because we have a deflicted front end strut/spring arrangement. K-members, or front subframe systems, reposition the the aspects of the car to increase handling and make undercar work easier. The jarring around you speak of is the notorious "mustang 2-step" oraxle shifting because your wheels are not independent of one another.Theres small ways tofix the car, and seeing as the Mrs. has a bun in the oven (congrats btw)heres a couple small improvements you could make.
1. Progressive rate springs lower the car, but because of their "progressive rate", maintain ride quality without stiffening up the ride.
2. Adjustable shocks/struts can allow softer setting with thefamily on board but a weekend at the track, you can stiffen them up.
3. Upper and Lower control arms may include stiffer bushings, but will heavily reduce your jarring around problem (and seeing the age of the car, they may have excessive play in the bushings anyways).
Companies such as
www.steeda.com,
www.maximummotorsports.com,
www.uprproducts.com and
www.griggsracing.com all specialize in mustang trackracing, you can buy parts from
www.americanmuscle.comtoo
And from what it looks like, G-trac stage 2 and some springs will be a great starting point, good luck