Hi there @Taylorscat !
Oh yes, getting used to Caroline's way of working out can be brutal, but it is sooooo worth it!!
Your plan is a good one. There's a fine line between challenging yourself and potentially risking injury. I worked myself up from 5kg to 10kg dumbbells over a period of more than 2 years, but I doubt I'll ever get close to the weights she uses. I often reduce the weight or modify/substitute moves during a workout.
Having a strong core is absolutely critical when working out with weights. Here are a couple of workouts you may find useful:
Bowflex 3-minute plank - I still do this every day
Rebecca Louise's Best Abs
Caroline Girvan's Braced Abs & Core
I found the Thighs & Glutes workout by Lucy Wyndham Read invaluable in getting my legs ready for Caroline's Bulgarian lunges.