Do you ever feel completely incompetent?  

Don't fret schilds. The sun will come up tomorrow morning and you will have a new day. Start with the language issue. No one will notice the dirty bird cage, but they will notice improper use of bad words. Issue a warning and then start taking favorite things away. After they see you are serious about the language issue the three year old will fall in line. I promise.
Don't let the two year old use a cup at anytime other than to get a sip of juice let them take their sip and return the cup to a place they can't reach. Use a sippy cup if necessary.
Don't put so much emphasis on a clean house. With small children a house is trouble to keep spotless. You won't be judged by how you keep your home. If you are judged by people for that, then consider the source and brush it off. Have the children take responsibility for cleaning up their own toys, they are old enough to handle this. If they leave toys scattered, pick them up and put them away so they won't be able to play with them. They will learn soon enough that if they don't do their job, they won't see that toy again for some time. When they follow directions return the toys but make them select which one they will get back. that will teach them that if their behavior is acceptable, all the toys will eventually be returned to them.
Laundry can be done on set days, and you can ask your significant other to mind the store while you do the clothes. If they refuse, then tell them they can do the laundry.
Dog poop should be picked up by your husband daily. Ask him to do it and don't take no for an answer. If he wants dogs then he needs to care for them and set a good example for the children. Same with the fish tank. You do not want your children to see that you are nothing more than a slave. Demand respect and tell everyone that there is a new sheriff in town and if they want to have the house cleaned, laundry done and the shopping and meals taken care of that you will expect help from them.
I know you are venting and may not be in a position to demand things like the ones I mentioned, but if you ask for help from your husband it will at least let him know that things aren't rosey there for you and he should step up and help unless hes a jerk.
the kids will follow your example too if you are firm and don't give in. It may take some time but if you demand more and expect more they will meet you half way in order to regain lost toys.
Good luck and I hope something I said here will make it a little better for you.