These kinds of relationships are always inherently difficult. Of course, she will, first, think she knows better because she's older and, second, feel defensive because she knows it's not her home turf.
Seems to me that you have two things to do first: 1. Make sure that your husband will be on your side and back you up as you try to be firm, and 2. Sit down and think about crafting how to respond to her (possibly taking input from a friend or counselor if that's available).
There are a few basic stances for responding, and you have to choose what works best for your temperament.
Some things you'll just want to express directly and earnestly, like saying, "Please, I'd appreciate it if you could give me a half-hour's breathing space when I get home from work." (Actually, my mother did that with me when I was a teenager. ) Similarly, you (and your husband!) can explain that it's the kids' house, too, and they get to be noisy - you can add that you enjoy the sounds of kids playing, and she should, too. And, by the way, why isn't it your husband making dinner?
If you can use a bit of teasing humor, that is great. For instance, if she comments on the dog's food being left all day, maybe you can say something like, "I was hoping that in your spare time you'd train him to wash his dish." Or, "Well, kids are kids and will always make noise - but we can give you some ear muffs for Christmas."
Another option is to be open about your being annoyed - but you'll call it being "hurt." As in, "It really hurts my feelings when you criticize me like that. Are you trying to be deliberately hurtful? Why would you say that?" Or, "Considering that I'm shouldering most of the burdens here, it really hurts my feeling when you sound so unappreciative and critical." It can help if you can burst into tears.
The racism is a tough nut. I once converted someone from being right-wingy to being left-wingy, but it was took about a year. I would just have short exchanges, and occasionally give him a short article saying, "This might interest you, apropos of our conversation last week." It's certainly worth a try. But you might have to end up saying as politely as possible that, in effect, you find her views not only antiquated but offensive, so it's better to avoid the subject for the present.
Good luck.