So it sounds like the SI joint is what the problem is. With the SI joint dysfunction I recommend doing the correction technique as needed/daily and doing the stretches/tens to manage the pain until the baby comes. As soon as you go into labor if you could do the correction technique that would be great, it won't hurt anything if you don't need it.
Good question as far as how long will it take to get better. The hormones from pregnancy cause it to be problematic throughout pregnancy, and if you breastfeed afterwards the hormones will stay until about 3 months AFTER you wean. Disclaimer, I am still nursing my son 2x/day and he is 15 months, so I am by no means suggesting that you don't breastfeed, just giving you a heads up.
After delivery I would get a serola SI belt to wear when you are taking care of your kids and then either go to PT or start core strengthening (pilates could help) once you are cleared for exercise. Once your core is strong, and the relaxin is out of your body, it should resolve, although you will be more susceptible to this problem throughout life if you step off of a curb wrong, or move from sit to stand on one leg instead of two feet.
Good luck with your vbac, please update us after delivery!