Trying to isolate one muscle of the trunk and blame it for the cause of any stabilization problem is a mistake. A lot of people do this and what they will end up with is strength imablances that will lead to more problems. There are a multutude of trunk muslces that all fire together to affect stabilization of the trunk during the squat. Both front to back stabilization and side to side. Just a cursory glance at "lateral flexion" will bring up the spinal erectors and the obliques but even then you wouldn't necessarily have the whole picture.

With what you are doing, having begun the Rippletoe, if you have a case where leg strength outwieghs trunk strength, coupled with the other problems you described, then, to me, it all comes down to being too heavy. In order to train the core musculature using functional movements like the squat you have to be able to maintain proper form and movement patterns. If those things are breakig down then you are "building in" incorrect patterns that will lead to and excacerbate these problems.

This program has you doing a lot of squatting and you are deadlifting. There is a place in it for assistance exercises for the back as well as the abbominal training but at this point anything you do is just as likely to be a detriment as a help.

It's always better to keep it simple. If you are wobbly during the squat then use a weight that you don't wobble on and build on it slowly. The strengthening of the core is paramount. It is the foundation of strength. If you take your time with the weight it will catch up. You can couple that with the abs, perhaps with the addition of obliques and maybe some reverse hypers.
But nothing overcomplicated. If you has been doing this for months my answer might be different but you said a few weeks. IMO, it is simply too early to be running into major problems so that leads me to believe it is too heavy.

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If you act sanctimonious I will just list out your logical fallacies until you get pissed off and spew blasphemous remarks.