Hmmmmm, sounds like you and your wife need to get on the same page or nothing is going to change. Set up some ground rules and boundaries together...then stick to them. I would also find out why your wife lets them walk all over her. Guilt? too tired to deal with it (believe me I understand, my 6 year old daughter has PDD-NOS, a type of autism)? My husband can be like your wife at times because he's gone a majority of the time (works a minimum of 70 hours in a family business). Although, since I'm the primary parent, my husband is good about telling the kids take it up with your mother or what did your mother say...he doesn't undermine me on purpose and it is extremely rare that it happens on accident (which if he lays down the law with our son, who he is much more likely to discipline I don't undermine him either; if we don't agree on a parent issue we discuss it when the kids are not able to hear it). Maybe your wife needs to work on why she lets them run the house. A first step would at least be asking your wife to see if she can adopt a policy similar to my husband's...let me talk to your father first or you know the ground rules state you have to have all clothes in your room put away before you can leave the house for social activities. I would seriously make these rules with your wife on a poster board. Then, post them somewhere. Having them may help your wife grow a back bone. I know from personal experience that alot of kids with special needs are given whatever they want because a parent or parents feel so bad...the kid takes advantage of it big time. Don't know if that is what is going on...just a thought. Best of luck and willing to listen anytime.

Sounds to me like you're being their parent and she's acting more like a friend. You and your wife need to relay a common front to the children or they will grow up disrespecting you both, not caring, and playing you against each other...and let's face it, our marriages have enough stress to deal with as time goes on without the added manipulation of teenage / preteen children. You two also have more on your plate with a preteen asperger's child. Try to sit down and talk to your wife about how now, more than ever you need to be a union when it comes to the kids, especially since it doesn't sound like you parent at the same time with your schedules. Try to be open minded about things you can be more lenient on...for example, here's a couple suggestions based on the examples you gave....
1. ROOMS/Cleaning...Chores in general: They must be done BEFORE going out with friends (now, bend when an opportunity comes up that's out of their control - like a last minute invite that's obviously important because it's their BFF) but for the most part - chores/must do's first...then play. For rooms, pick a day a week THEY clean for real, besides day to day make your bed, clothes into hamper...one day a week DUST, VACUUM, etc. your room...don't care WHEN, but it's to be done on that day. :)
2. IPOD/IPAD/PC/TV/Video Games - 1 hour a day during the summer before dinner. That's what we've had to do...now, we aren't super strict about it, but we told the boys, they really should get out more...:) We stick more to the no IPOD at dinner, no IPOD at the store, or during 'family fun' times like evening walk, watching a movie, etc.
3. If she lies to you about doing chores/picking up clothes and you find them, well, bag them all up in a black garbage bag and put them in the garage...remind her...your house, your rules. Please clean up your room next time before you go to a friends house.
All of these things you should discuss with your wife and get on the same page - remember, they are growing up and you do have to let them see friends and allow them room to develop trust and responsibility. Good luck! I'm sorry you're going thru this preteen bumpy road time right now. :)