I feel that the only reward for sitting in this scenario should be coming up on the couch (a life reward). You want her sitting when she wants to come up, not sitting because she wants a treat.
If you see the dog wants to come up I would block her. Don't ask for anything. If she happens to sit move aside, pat the couch, act all happy. If she jumps up say "up" or whatever invitation word/hand signal you choose to use. If when you block her she chooses to walk away then that's fine, she doesn't get to come up, there's nothing wrong with that.
Similarly with crossing streets, just stand and wait. Yes you might look odd to passer bys. Yes you may confuse some cars. If they slow for you shake you head and wave them on. As soon as that dog sits, click (or use a marker word), pull a treat out of your pocket, and give a "let's go", then cross the street. Don't try and get her to hold it for extended periods yet, that can come later.
Work on sits seperately. You must get rid of that bribe. Bribes are the reason Tucker listens to my mom in puppy class and not at home. At puppy class he sees a treat, at home he sees nothing and gets nothing. He listens to me at home becuase i have treats in my jeans at all times. A good chunk of the times he obeys me I pull a treat out for him. So he never knows whether or not he'll get rewarded. With mom if he sees a treat he'll be rewarded, if he doesn't, he won't. Simple logic.
I would completely start over training it. Perhaps just to start, put her on a leash. Sit in a chair and just look at her. Either have the treats in a bowl on a table next to you (positioned far enough back so that she cannot see it) or in your pocket. If they are not pocket friendly (they are wet like hot dogs or something) then have them in a baggy in your pocket. This is assuming you are using a clicker. When you use a clicker there can be some lag time between the click and the treat in which you can yank the baggie out of your pocket and get a treat out of it.
Eventually the dog will get tired of just standing there and will likely sit or lie down. If she lies down get up and walk her a few steps so she stands back up, then sit back down in your chair. Continue this until she sits instead. As soon as she sits click and liven right up, lots of happy words, jump to your feet (all the while getting your treat for her, use long happy strings of praise between the click and treat). Give her the treat and try again. Once she catches on that you want her to repeatedly sit stop sitting back down yourself otherwise this will become her cue to sit. If this stumps her just wait again. Technically you never had to sit in the chair in the first place but some dogs can take a really long time to catch on so sitting can keep YOU from getting frustrated.
Once the dog sits, gets treat, sits, gets treat, over and over you can add in a word. Right as the dog goes to sit say "sit" and click/treat for sitting. I'll usually be able to add the word in one session but will not start using it right away in the next. The dog doesn't usually know the word during this first session. In the following session you will start as before, just waiting. Click and treat for sits until the dog does them repeatedly, then start adding the word again. Say sit, click and treat for sitting, walk away so she follows you, say sit again, click and treat for sitting. Eventually you'll want to start switching off between the sit and another behavior he knows so that you can really see that he connects the word to the behavior. If she doesn't know any others then teach one seperately and try switching off later. If when you try and use two commands in the same session the dog gets really confused you can be fairly certain she doesn't know the words yet so you have to go back to where you were before, saying the word as the dog does the behavior.
Only after the dog really seems to understand the command during training sessions can you start to use it randomly around the house. I would constantly carry some sort of treats (in this case not ones that need to be refrigerated) in your pocket. This way you can spontaneously ask for something and quickly reward from your pocket. DO NOT reach into that pocket until the behavior has happened or else you are still bribing. You do not have to carry a clicker as it shouldn't take too long to get the treat from your pocket. But start praising as soon as the behavior happens until you get the treat to her. If she ignores the spontaneous command you can try just standing and waiting to see if it happens or just know she's not ready for it and don't ask again for a few sessions. Remember to have practice sessions all over the house with you both sitting and standing. It is only at this point that you could request a sit before letting the dog up, which is why I recommend just blocking and waiting for now. If by the time you are to this point she isn't asking yet, feel free to start using the command.
Anyways that's how I've done it. Also be aware you can do some luring without it being a problem. For instance I have to lure roll over. It could be shaped but would take FOREVER. But after four or five rolls in a row I stopped having the treat in my hand and after one training session the treat was never in my hand again, it was in the baggie in my pocket until after the click. I still used the exact same hand motion but no treat. The allowed lag between click and treat is one of the great things about clicker training, USE IT.
Sorry for the excessively long post, I like to be...thorough
