That's a very interesting situation, and I wish I responded earlier in the day.
First things first, go ahead, accept the position, the current PM is toast anyway, and he will probably be fired, there's nothing you can do about it. He just didn't do his job.
Your great advantages is that management trusts you, and you can use that trust to your advantage, especially when dealing with the project team. You need to bring up the current situation of your project team so that your project sponsor is aware of the issue (she may give you some advices or she may take some prompt action). In any case, I'm sure that your sponsor will give you a "Carte Blanche" when dealing with your team members.
Your next step is to deal with the project team, and this is the hardest part. My guess is that they're not taking you seriously as a project manager. Try to be professional with them as much as possible, and set aside your feelings. Now, you need to re-do the whole thing, re-estimate the tasks after consulting with your team members, and then re-assign the tasks to your team members. In other words, you will need to create project out of the remainder of the project. Once you re-start the execution phase, you will need to micro-manage these team members, and continually assess their work (and the quality of their work), especially in the first few weeks. Forget about cultural differences, that's not the problem, the problem is that you have a bunch of slackers who don't want to do any work and would like to sound stupid rather than doing actual work.
If, after the first week (a week is more than enough, no need to waste more time on them, there are plenty of people in need for a job out there), you see that some team members are still giving you hard time, then fire them/take them off the project immediately and hire others in their place. (you will not miss them trust me, the project has reached this point because of these slackers, as well as the project manager) The new project is still in its beginning and there won't be any overhead when switching programmers. I personally suggest you start looking for new programmers now, as I believe that attitude is non-changeable.
If you think that you should ask for contract re-negotiation, then this is what you must do. The client will not like it but he will respect you even more for that. Of course, you should advise your project sponsor before doing that, and don't let her pressure you into accepting the current contract.