Megan, you are describing my situation nine years ago -- except that in addition to be a fat diabetic, I was also "geriatric" new Mamma. While I was pregnant, I was able to keep my sugar down under a 5.1 hbA1C -- but once I started breastfeeding I started to gain weight and had a terrible time controlling my blood sugar. I went on metforman and started taking insulin again for the duration. After my little guy weaned me (just after his third birthday) I started having even MORE trouble. Went to the doctor who increased my insulin --wash, rinse repeat. Three years later, I discovered PB. It took a while to get my blood sugar under control...in part because I was taking *too much* insulin for my body's needs, forcing my body to dump sugar just to keep me opn an even keel.
My advice, knowing what I know now? Tend to baby and your other needs, eat as primal as you can, and take whatever insulin or metformin you need to keep my blood sugar decent. (You're quite right about wanting to keep your sugar under 120 most of the time, but it may not be possible without meds and insulin for the moment. Do your best and realize that it's only a few years.)
Eating primal is best for you and baby, as is keeping your blood sugar uner control in whatever way you can. As you've noticed, lack of sleep is a big factor in the wild BG swings in the early days.
BTW, congratulations of keeping such excellent control during your pregnancy despite the doctors orders! That took a LOT of work!
Grain Free since 2009, WP from 2005
~100% primal (because anything less makes me very sick)
Goal: hike across Sweden with my grandchildren when I retire in a few years