Welcome Blue, you will find this issue in many posts. Your wife is the problem not the child. United parenting with proper direct consequences is how little children learn.

I am a disciplinarian by nature peppered with lots of love. I parent in a united manner with my H towards my daughters. One biologically his and the other not. So for example if my H tells my 7 year old she may not have pudding, whether I agree with it or not, then there is no pudding. Children will divide and conquer.

So your wife needs to decide what role you play in your SD's life. Once she has decided that, you jointly need to decide how you parent this little girl. Or not parent as it were.

Have a read through these and look at the principle of I ask with a reason, I give 5-15min for compliance dependent on what I have asked, I ask a 2nd time and give a further 5-15min. If I am still ignored I time out.

Scenario:

Mon: Polly you need to tidy up your art supplies, it is almost bath time
I wait 10 minutes for her to do this and return. If done I do not time out as she has complied. If not done ...
Mon: Polly this is the second time I am asking you to tidy up your art supplies, it is almost bath time.
I wait 10 minutes for her to do this and return. If not done ...
Mon: Polly I have had to ask twice for you to clean up your art supplies and you have not done so. You will go time out now for 7 minutes.

All of this is done calmly, without raising my voice.

If Polly defies a house rule I use the above method but the warning can span 3 days. Example my children may not put shoes on my couch. Yesterday I warned once, today I have warned again and tonight Polly puts shoes on the couch. She goes time out.

If Polly endangers her life such as your above scooter scenario then it is immediate time out without shouting. Endangering their lives is an immediate consequence.

Your wife MUST support you in this or you do not take SD for scooter rides. It's not acceptable behaviour and trust me your wife would never forgive you if her daughter was harmed in your care.

http://www.amazon.com/1-2-3-Magic-Effective-Discipline-Children/dp/18891...
http://www.123magic.com/
http://www.askdrsears.com/topics/parenting/discipline-behavior/10-time-o...
http://www.parenting-ed.org/handouts/timeout.pdf

Good luck and let us know how the talk with your wife goes.

Skipping ahead, this just happened within 30 miles ...

http://www.9news.com/story/news/traffic/2015/10/08/garfield-57th-street-...

My first piece of advice would be to pick and choose your battles very carefully.
Telling her that she was reading the book wrong, not battle worthy.
Teaching her street smarts and her defying you ? TOTALLY battle worthy.
I would never suggest that you disengage from scenarios that might bring about an argument, however, as you're going to read, over and over and over on here, first and foremost what MUST take place, is a conversation between you and your wife, and as Monchichi stated, you have both got to be on the same page and her emasculating you has GOT to stop.
I'm curious....if you've lived together for a long time before getting married, were there no scenarios requiring discipline before now, or did things just change when you said "I do " ?

Good parenting advice from some great parents above. Yes, you do need to make the child respect you on your own two legs (take the scooter away/end the walk etc.) and you do need your wife's support. If you can't do both these things, stop being alone with the child. Children need authority. You need the kind that is personally yours. Since you are a stepparent, you also need the kind that comes from mom endowing you with it. That means dw says to kid, "I know you will be good for Bluebox, I expect it." And then she backs you up when you need it.

I do have a concern that your wife is misguided in her own parenting. Why is it "you don't know how to talk to kids" that's coming out of her mouth? Why does any 5 year old feel empowered to snub an authority figure? DW may need a parenting class herself.

When my ss acts up in school I tell him the teacher worked hard and he owes it to her to behave. I NEVER say "oh, teach, you don't know how to talk to kids!"

Hello,

I treat my SD like my own and my wife knows it. So if I yell at SD and or punish her, I'd do the same with my DD. So she always backs me in all my decisions but may tell me behind closed doors that I could have handled that situation a little better. Like you, I got on her about her reading and writing. I made her rewrite her entire homework assignment the other day because I couldn't even read what she wrote. I tried to have her read it and she couldn't either. So she got all pouty and cried. I told her that it's my responsibility to make sure that she can write legible and have the proper grammar. So I let her sit there and cry, when she was done, she rewrote it the way it should have been. Her mother sat there with nothing to say because she knew I was looking out for the kid and it was the right thing to do. Your wife should have supported you just the same.

As for the bike thing, before we leave the driveway, I tell her the rules and if she breaks them, I'd pull her off her bike and she can walk home. I don't care about her feelings when it comes to her safety. I watched my wife do the exact same thing to her and her little friends when they rode out in the street without looking both ways, it was in front of the other kids mother. The way she saw it was, if you're not going to say it, I will.

I agree that your wife has created the issue more than the child. She is a child and of course is going to test boundaries. If she knows you don't have the final say with her or full backing from mom then she will walk all over you. It's not her fault it is jus how kids are. You need to be able to set the rules and stick to them. You wife needs to support your decision with the child and can discuss the details in private. Once she realizes that the two of you are united then she will stop. Having said that, you have to give the child time to adjust to the new authority figure in her life. Instead of drawing a line in the sand for unimportant things let them slide. If she deliberately reads the book wrong either ignore it or make a game out of it. The more serious issues are when you establish who is in charge and then when little things come up its not a big fight. I have always maintained there is no rational reason to argue with a child. I refuse to do it.
My DW is really incredible. She has a very difficult son whom I met well in advance to our wedding. I told her she needs to let me discipline him or this will not work. I have two fantastic children now and I wanted similar expectations. She agreed and basically let me take the lead and never questioned me in front of him. He had a serious behavior problem acting out in extreme ways. He does not do that anymore. We have new issues but the point is the only way it works is if both parents present a united front to the children. My wife and I argue about how to parent all the time but we come to a consensus and that is all the children see.

The problem definitely is your wife. She needs to understand clearly that when you married the two of you became equity life partners and that makes you both equity parents to any children in your marital home regardless of kid biology. DW blaming you for disparate behavior of the 5yo when with you and with DW is telling far more about DW than SD.

I would not let this go much longer without a focused sit down, face to face, to get alignment between you and DW.

As for SD not listening and behaving in ways that endanger her safety.... nothing a swat to the ass won't fix.