Y.L.
First, my heart goes out to you. There are a few of things you need to address here:
1. You and your husband need marriage counseling and if that does not work you need to leave him. Having a non-supportive husband and one that puts you down is worse than having no husband at all. You think you can't do it alone but you already are and being with someone like that is more harmful than being alone. Hopefully you can get him to marriage counseling and it will work.
2. You need a different pediatrician. There's absolutely no reason to let your child cry it out, especially if it makes her throw up (it almost did that for my son and we dropped it after 3 nights).
3. If you brush your kid's teeth after the last meal and then only nurse afterward, then nursing at night will not damage her teeth.
4. My son went through the same phase. This is what worked for me which is not to mean it will work for you but you could give it a shot - I started giving him a '2nd dinner' about half an hour before bedtime. It is usually an oatmeal/cereal type meal with warm milk (breastmilk or formula or whole milk). I warm the milk first (I do a cup of milk for about 60 seconds in the microwave) and then I add one spoonful of cereal at a time and mix until I get a thick but not lumpy consistency. I also add about 1/2 a spoon of raw sugar and some cinnamon to make it taste better. Or if he doesn't want that I'll give him yogurt and some cheese and some apple. I make sure to brush his teeth after of course. Then we do our bedtime routine and I stay with him until he falls asleep. It might help to get her out of the crib and put her mattress on the floor or get a twin mattress like we did so you have room to lie down next to her until she falls asleep. This will give her the confidence that you are there for her. If she wakes up at night hungry in spite of having that 2nd dinner, first offer water (it would be ideal if your husband could go to her and offer her water because if it's you of course she wants the breast, but it seems unlikely that your husband will do that; that's something you could discuss in counseling for example - him actually helping with the kids). There have been times when my husband was out of town and I just had to nurse him at night because he wouldn't take water from me. I also keep a small container of cheerios and a cup of water by his bed so that if he is still hungry he can have some cheerios and water instead of nursing. He stopped nursing at 21 months. Of course I don't brush his teeth again in the middle of the night if he eats, but I do right after breakfast. So those are my suggestions. I doubt that she's really hungry. Just some water might actually do the trick. If you believe she really is hungry try to gently but firmly tell her she can have cheerios and water but not nurse. It might work it might not.
The main thing though is that you and your husband get help. You cannot go on living like that. You will spiral into deep depression and that is just not fair to your kids. She might be even sensing that stuff isn't right and that's why she's waking up at night to make sure you are still there with her. Your children have to come first and for that, you need to come first. It sounds like between making all the meals, going to school, and working from home that you do a WHOLE LOT and so your husband sounds like a real jerk. Sorry to be so blunt but if he won't go to counseling you need to get rid of him because he is setting a bad example for you kids and causing you depression and that's just not the right way to go through life. You deserve better than that.