I don't actually think your wife hates your daughter. She obviously hates some of your daughter's behavior, and is frustrated with you that you don't try to change it, and instead just accuse your wife of being the one in the wrong. Being a Stepmom is HARD, and frustrating. She is raising someone's kid that she had no say in instilling manners in, etc.

Have you considered your wife's happiness in this? I would say you should step back and ask yourself- is it really a big deal if I tell my daughter to put her feet down, have some table manners, and not wake us up in the morning or come in the bedroom? Will it really hurt my daughter to agree with my wife on these things? They are not unreasonable expectations. Your wife obviously is big on manners, and doesn't want your daughter waking you both up in the morning, or being in your bedroom. I wouldn't either! We have a rule, skids cannot knock on the door in the morning unless it's an emergency. They are not supposed to be in our bedroom. This is pretty standard, and normal.

As far as putting her feet up and eating with a fork properly. Why wouldn't you want your daughter to eat properly with a fork? It's your wife's house too, and this is a CHILD. If your wife, who is the adult in the house, doesn't want a child to put their feet up, then tell your daughter no, and don't make your wife continue to do it! Again, this will not kill your daughter.

Now, if your wife is honestly just being hateful to the daughter for no reason, that is a different story. These examples you have given are not out of line though. Sometimes Bio dads have a tendency to think their kids can do no wrong, and should be allowed to do whatever they want, while the Stepmom is the b*tch for calling them on crap and expecting manners and respect. Bio dads don't like to tell their kids no, and just let them do what they want because it's easier that way and they often times have divorce guilt. Don't be that guy. Kids can be told no!

my daughter I see only weekends when she’s here with me...

When my 2nd daughter was born with my wife due to circumstances the baby was taken from her and given to me

I'm confused. One lives with you? One lives with the ex? Same mother or different mothers?

You have 2 daughters? Who are the moms? 

Are you saying you had a second baby with your first(ex) wife recently and your current wife is in charge of both kids?  

Or is this a "first" family story and your wife grumpy to her own daughter?

I have an 11 year old daughter. Or almost 11. She will be 11

in one month. I would be horrified if she was eating with her feet on the table. I would say something to her and I am her mother. My 11 year old is going to go places in this world and I don't want her embarrassing herself at dinners with professors , bosses, clients, etc. Children need to be corrected and learn table manners absolutely.  

I am confused. You have an 11yo daughter with your wife and a second daughter with your "wife" who lost that daughter in a custody battle with your and you are married to yet another "wife"? 

So, you had your second daughter  with your first wife or your current wife or a wife between the first and current?

Now for the issues between your "wife" and the 11yo.  Table manners, not putting feet on furniture, etc... should be a given and should be standards of reasonable behavior required in the home.  You need to be enforcing these as firmly as your wife is and wishes that you would. If we had our elbows on the table while eating we got thumped in the elbow with the handle of a table knife.  That hurts let me assure you and rarely did it have to happen twice in our lives.  Heaven forbid if we had put our feet on the table like some kind of pig beast of a rude crotch dropping. My  brother's children used to pull this crap and when they were visiting my parent's home the shit hit the fan when they did it at my parents table. My dad went ape shit on them and on my brother for raising rude little shits.  My SIL got all offended and my dad told her to get out.  It took hours of discussion to calm things down ... but... never again did my niece and nephews do anything at my parents home or  table other than sit properly, use the eating utensils properly and speak respectfully to my parents.

And for the 11yo violating the marital bedroom to wake you and your wife up regularly.... only if it is an emergency.  The marital bedroom is a sacrosanct area that kids older than about 4-5 never violate without invitation.  The 11yo can knock quietly and if not beckoned in... she can leave.

Now for the "emotional hitting" . If this includes physical violence, the next time she hits you... toss your hopefully STBXW out in the gutter, call the locksmith to re-key the locks and move on. 

The baby was taken from your wife and given to you and you are in court getting it straightened out?  Sounds like she had drugs in her system when the child was born or had a previous abuse issue.  They generally do not take children from women at birth unless there is a major issue.  There is more to the story here and I would guess that the underlying issue has a lot to do with what is happening with the older child.