The thing is a stepfather is just like a father and would have to discipline his stepchildren however he would do his own children. The only difference is the way people look at his behaviour. Many would say that a child would be disciplined by his Father but verbally abused by his stepfather. So this is where the support comes from the Mother. The Stepfather is to show no extra leniency towards a child because the child is not biologically his. The same way they will always turn to the mother for leniency and this should always be avoided as this will create two sides for the child to choose when there should by the one side (both mother and stepfather combined).This would end up in the child taking advantage of the situation. At the end of the day, a stepfather is expected to show the same love, lessons, and discipline as if it were his children. If a stepfather is expected to show love, he must also be expected to discipline. Children are sweet and are bundles of fun and this does not come easy. Hitting is not something i would suggest but rewards and benefits are usually the best way to teach and discipline. Once the children can understand that their are certain things that they have gained by their own hard work and that it can be lost due to bad behaviour then you would find that the teaching process gets easier. They stop testing and start thinking of their actions.
However you two agree he should! The first step is to sit down with him and the kids, and you explain that he is an adult in the house, that when he married you he also took on the role of raising them, and that they need to show him the respect he is due. Then you review the house rules and tell the kids that when he issues a consequence for bad behavior, you support him so there's no point in them coming to you to complain. This shows him that you support him and believe he can make good decisions, and it shows your kids that they can't play one of you against the other to get out of trouble.
Sometimes the best you can do is let her cry and scream, I know it's har because sometimes you just can't take it, but once she sees that getting her way is not working out, she will see she better do things the right way. If you send her to time out (for example) and she starts craying, leave her there, and leave her there till the 5 or 10 minutes are up. You can put her in a room and stuff. Count to 3 if she refuses to go and tell her if she doesn't her time out time will go up or she wont be able to play for a longer time.
By doing what a father would do? A 6 year old, could be diciplined by not letting him play with her toys, video games, or whatever she likes to do with her free time. Go to time out, and then have her explain what she did wrong and what she will do next time, no dessert for the night and little stuff like that. For a 10 year old, it could be stuff like taking the iPod away for a week or two, taking video games away, grounding him, no television, no music player, and just stuff like that.
All of this generally works with my 10 year old, the 6 yer old however is a bit more difficult, she actually is very determined to get her own way, and just screams when we try discipline methods that you said above