Take control. Children aren't born knowing the social rules, it's up to you (both of you!) to teach them. So be firm. Send them away to clean their hands, hell, have a hand inspection if you have to!
Re your husband, tell him that eating like a pig is deeply unattractive!
Keep the bread in the freezer and take it out as needed slice by slice, so lots of bread isn't available at the dinner table!
Teach everyone to eat more slowly. Eating too fast causes sloppyness and mess. It's the shoveling it in like someone is going to come and take it away from you that does it! A good tip is to put down your knife and fork between mouthfuls. This also stops you overeating because you aren't eating so fast and your stomach gets the signal to your brain that it's full, before you are stuffed!
Re the farting, unless she has a medical condition then she bloody well CAN help it! Send her out of the room every time she does it! "Go to the toilet and come back when you have finished breaking wind." Get her to go to the toilet when she feels the need to break wind, instead of doing it at the table. It's not nice when you are trying to eat to have to cope with that particular smell!
At the end of the day, how the children behave is down to you, good or bad it's how you've shaped them. And you can change it. (and that 'you' is both you and your husband btw, although if he is setting a bad example it makes it harder. You need to tell him how revolting his table manners are.)