I am a new mom, financially savvy but am suffering from the mistakes of my past. I did not have good financial role models in my parents, and as aresult, got sucked into poor credit card use in college. So I was off to a bad start there. Then, after college, I had a bad break up that left me broke and therefore, defaulted on my student loans. This black mark on my credit makes it impossible for me to get any credit, or to help my husband, who had amazing credit... until the credit card companies saw him as a risk (he is on our mortgage alone) and cut his available credit lines in half, jacked up his APRs and dropped his credit rating out of the high 700's to high 600's. My score,as of today is 590. I have no open credit cards, and am only paying off my car loan and student loans. (totalling about 43K)
What do I do here?

My situation is a little different than yours because my credit score is low simply because I haven't had much credit history good or bad yet. But I was told that the best way to keep improving my score was to just keep making my loan payments on time. And if I had any credit cards to not use them but keep the accounts open with a zero balance. Or if I had to use them pay them off right away. Basically it doesn't seem there's any quick credit score fix...

I am going to go with a potentially unpopular response and say "live without credit"

You already have a house. If you are using credit to live day to day you are just going to make it worse, not better.

Everything else you can live without.