One of my wise teachers had a saying I’ve always kept in mind: “Never attribute malice to what is merely stupid.” Yes, you did something that was thoughtless. But your mother-in-law’s reaction is way over the top, especially since you’ve apologized. Your husband is caught it the middle, poor thing. My guess is that this is an old pattern with his mother and he’s done his best to avoid getting into this kind of situation with her. Unfortunately, you walked into it. He probably doesn’t know how to support both of you.
So — my suggestion is that you apologize to your husband for inadvertently putting him in a tough spot. Ask him to tell his mother that he is not responsible for your slips, that you’ve made your apologies and now she needs to deal with you. Ask him what he thinks of this suggestion. (He does know his mother well, after all.) — Take the sign down. Send mother-in-law flowers, let her know that you now understand how the sign could be insulting and you’re sorry. Then add that it would be sad if she didn’t want to get past this but you’ll respect her decision and will wait for when she feels comfortable talking to you again. Then wait. To make more of this only makes things worse. My guess is that in a week or two, things will calm down and she’ll act as if nothing ever happened since she doesn’t seem to be the type to talk things out.
I wish you luck with this. If she insists on staying mad, there’s really nothing more you can do except hope that time will heal.
I wish you well.