Any Canafian mom's take disability leave and maternity/parental leave together??

I am sure I will get more info from my HR lady at work later but I JUST spoke to her and found out I qualify for an extra 4-6 weeks disability leave on top of 15 weeks maternity and 37 parental. But I am trying to figure out how that works... From my understanding maternity leave HAS to start as soon as baby is born and I presume I can't start disability leave until baby is born either (as it is 4 weeks for a vaginal delivery and 6 weeks for a cesarean). But parental leave must be completed by 52 weeks after baby is born. Which leaves JUST enough room for 15 weeks mat leave and 37 weeks parental.

I am wondering if anyone has taken disability with their maternity leave before? Does this mean it could be taken before birth? Or my hubby should take the 4-6 weeks out of parental to make up for my disability leave time so we don't lose out on time? Or perhaps disability leave and maternity leave overlap and you get the benefits at the same time? When combined with mat and parental leave perhaps it is only a monetary benefit?

Again, I'll be talking to my HR lady again later it is just really bothering me right now - I want to know how the logistics of it work.