It’s good that you have decided to start working abs before it’s too late, but only after hurting your back. The initial question is 'was it the deadlift that hurt your back (bad form), was it a result of another weak link (posterior chain), tight muscles or a result of weak abs?
Sometimes it can be one of those things or a cumulative effect of one or more leading to your back hurting. I need a bit more information such as did it happen during the deadlift or did you feel it that day/next day? Was it a all-out max set or just a general warm up? That would be good to know.
I will try to answer your questions as best I can with the information provided.
Should I do ab work at the end of my workouts and simply up the volume?
Ab work is best done at the end of your workout, otherwise you’ll fatigue your core musculature and that’s the last thing you need when you squat or deadlift. I’m not sure what you mean by ‘up the volume’ as you haven’t listed your current volume. I do 4 exercises in a row for 2 giant sets, so 8 sets total. That’s twice a week on lower body days and that’s more than sufficient. I never use a belt to also help to engage my core.
Should I stop doing lower body work for two weeks or so and work those abs aggressively?
I wouldn’t neglect lower body work and focus on abs, but maybe you would benefit from a deload week or two. Still train, but at a reduced intensity. It also depends on whether you’re actually injured or you’ve simply tweaked something.
Can I do ab work in between sets of deads and squats, or is this an unreasonable thing to do?
I’ve answered this in the first question, but it bears repeating again - NO, I would not do ab work inbetween those two major lifts.
Overall, I would recommend stretching your lower body (calves, hamstrings, quads, hips, ankles) and your lower back. A brilliant and ery cheap aid would be a foam roller. They really are amazing and very neglected for helping to prevent injuries, as well as treat mild existing problems. Work on that core and don’t neglect the obliques or transverse abdominis (the muscle you use to breath in your gut when a hot chick walks by).