I had a copper-T IUD inserted, which is similar to Mirena, after my first child was born. My period had not yet returned. I started bleeding very lightly at first, then heavier and heavier over the course of a month until I was bleeding heavily every day and concerned I was hemorrhaging. At the end of a month I got a week-long migraine, and my OB said this was all likely just from the return of my cycle, but I didn't want to take the risk and keep bleeding, so I insisted he remove the IUD and we decided to take our chances with birth control (since I'm not consistent enough to make the pill effective and I couldn't use the patch because I was nursing). Within a day of removing the IUD, the bleeding stopped, and so did the migraine. Granted, I get migraines anyway, but I'd never had such a persistent one. My OB assured me that such a response to the IUD was rare, but I'm glad I insisted on having it removed, because the risk of an unexpected pregnancy was less worrisome to me than of continual bleeding and other complications. (And I got pregnant again when my son was 9 months, so we now have TWO boys!)
So, I'd recommend removing it, because so much bleeding is not healthy for you, and could lead to worse things. :) Congratulations on your lovely family!