Big (((Hugs)))) on getting DH to follow BW. I so know where you're at. I had the same trouble convincing *my* DH. Here, I had read all the BW books and even become a mod and he STILL thought his ideas about sleep were right based on the fact that...well, they were his ideas! No books to justify, no evidence, no putting it in practice. He just simply thought he knew how it worked, so there. It probably wasn't until my son was about 2 that my DH finally understood the whole OT phenomenon -- up until that, he just thought I called ALL sleep problems OT! LOL!
I would make a deal with your DH. Tell him that you want to follow this new routine for 7 days. YOU will get up with her at 4:30 in the morning if that's when she wakes for the day. If after 7 days it's not helping, then you'll try his crazy idea of a 2 pm nap etc. But ask him please, please, PLEASE to commit for the 7 days. It can't start working until you start doing it! And right now things are only going to get worse in an OT cycle. I really believe that will make all the difference for her. Also, tell him that 10 hour nights is a classic OT sign (not that he'll care) and that she really should be sleeping 12 hours at night. Since he's a man, he probably thinks 10 hours is a long night for a child (since as adults we only sleep 8 max) -- so he may not even be aware that your goal is 12. Let him know what the sleep goals are and just ask him to commit for 7 days with you. Now that you're well, too, you won't be as dependent on him doing the sleep stuff.
HTH!