I'm going to go on a limb here and tell you my honest opinion. I don't blame you if you take it or leave it.
You resent your mil because she has "plenty of time and money." All your posts are full of dripping malice in references to your mil's money and lifestyle.
Look, you are still grieving from your husband's death. The pain you feel has nowhere to go...you are spending your time caring for your children, worrying how they are doing emotionally, and caring for your husband, also newly grieving. The pain has to go somewhere, and here are two people, your pils, who seem to not know what pain, worry, grief, thought for others, financial struggle, or work is. Thus, you're taking out your pain and feelings on them, they are perfect for your anger because in the year and a half that you've known them, they haven't been awful, but they haven't supported you in the way you think they should. You couch a lot of your complaining in the guise of being angry at mil on behalf of your husband and children, but a big part of your posts is that you hate that mil has money, no worries, parties and French classes, while you make "sammies" for your kids and listen to your dh complain about his rich mother.
Some day you both will have to come to terms with all this. Otherwise you both will be miserable for years and you'll miss out on the joy of your children being young.
You'll be happier with yourself once you recognize that your mil is not responsible for your grief. You know this, that's why you're conflicted, you know they're not horrible people, your mil is someone to project your pain onto and you are doubly intensely angry that she is seemingly unaware of even your hostility toward her. She is living her life with joy and you can't stand that, you want to smack her. After all, you've suffered and she hasn't and she deserves to suffer.
Your husband will have to come to terms with the fact that he is a grown up now. He's not a little kid who is at the mercy of his parents. Either he should have the guts to go no contact with them (I had to do this with my own inlaws, truly evil, you would not believe), or tell them honestly how he feels about how he's been treated his whole life and see if they will apologize and reconcile fully (I actually did this at the ripe old age of 34 and the persons concerned did indeed apologize and made things right, it was a major relief and joy for me to fully reconcile), or he will have to accept who and what they are and who and what he is and move on. He's chosen to hold them responsible for his hurt still and you've followed suit. Are you both afraid to go no contact in case you won't inherit her wealth? I bet you are seething, having to be civil to someone you despise (for not a great reason in my opinion--there are mils a thousand times worse than yours) so that you won't rock the boat with the inheritance.
You're not happy. I think you'll only be happy when you come to terms with the unfairness of what has happened to you and your family, treat yourself kindly, and treat your mil kindly. Try being happy for your mil and allow her verve for life influence your own thinking...the ironic thing is that I'm sure you are truly a kind and generous and normally happy person yourself, and the injustice and sadness of what's happened to you has made a dark place inside your soul. I feel for you and what you're going through...take heart. In a way your dh is making it worse for you with his complaints. If I were you, I'd tell him it's time to move past recriminations with his parents. Then both of you will be able to move on to happiness. You may even find joy and hospitality and support from your mil once you make peace with yourself. Keep us posted, good luck 