The good news is that it seems like your cervix knows what to do! That's great and can be normal - even this early - especially if you've already had one baby. You're concerned because you don't want to go into labor too early and have a premature baby.
I'd ask your midwife to do a fetal fibronectin test. This is a simple painless test that can be done right in the office, and accurately predicts if you will or won’t be going into labor in the next 1 - 2 weeks.
Many women can walk around dilated 1, 2, or even 3 cms for weeks before delivery without any problem. But you'll probably sleep better having the test. I hope you have a healthy delivery.
If you’re getting ready to head to the hospital, check out my free list of what to bring to the hospital.