So here goes,
The setup:
My wife and I had our first child last April.
My wife runs a business with her mother and sister. It keeps her busy pretty much at least 6 out of the 7 days of the week. Many of these work days she is either going in around lunch time or coming home around 3pm-ish. I grew up in a day care that my mom ran and my closest sister has six kids ranging from 13 down to 2 and I would like to think I have played an active role in their upbringings. The point is, I have been around kids and general child rearing and feel as though I have a little bit of good parenting knowledge. For me, it feels like the kind of thing that just sits as that kind of subconscious knowledge at the back of your head that lets you know what to do without having to deliberate consciously. My wife on the other hand seems a little bit overbearing at times and simply can't let the baby down for very long at all. This has turned my daughter into a little girl at 9 months who seems to need to be held more than I am accustomed to while she should be rolling around learning to crawl.

I work long hours, leaving for work around 6am and returning around 6pm daily. I feel like I do what I can in terms of diapers and spoon feedings but my wife won't use formula and insists that it makes my daughter sick. I love my daughter more than anything and I think we DO have a good bond. I have the knack of squeezing a smile out of her that no one else has and for me that feels like my own special place. However, while I know that there is no sub for mom, nor should there be, I can't seem to be all that my daughter needs for long enough time to give my wife a break. She is repeatedly exhausted both emotionally and physically but our child has become accustomed to mom and mom only as a solution for every little need. I know my wife well enough to know that she wants to be able to read, exercise, maintain the household and all sorts of other things that she would do if she could learn to multi task with baby.

Now I have to admit, neither me nor my wife have ever been the best of housekeepers. We tend to let dishes sit in the sink, vacuum too infrequently, and own too many clothes because neither of us do laundry often enough and rarely fold-and-put-away clothes when we do. I don't want to give the impression that we are slobs, we just tend to let things stack a bit and then be forced to spend hours infrequently rather than minutes frequently to catch back up to cleanliness. The effect of our habits have worsened with the kid and I really hate the home that we are raising our daughter in. Recently, I have been going on cleaning/chore frenzies in anger and don't like the tension I feel towards my wife during them. I shouldn't make myself out to be the hero either because sometimes it just doesn't get done because I'm too beat from work. We probably need to hire a cleaning lady (perhaps a little difficult to afford but not out of the question) but I think that there are underlying issues that should be addressed.

1. Should I let my wife 'find her own way' as a mother or should I actively try to help her learn to multitask with baby.
2. Should I try to change our living habits to do more maintenance cleaning. Seems like a no brainer but it has always taken on the form of flailing new years resolution in the past. I could use some suggestions on how to actively accomplish this.

I suppose most of this is just thinking out loud but I'm sure someone has experience with this.

First, ask your wife what she would like you to do to support her while the baby is still so dependent on her. Before you ask though, do the obvious things - don't make her tell you what you can figure out on your own.
Don't criticize her but open discussions with her like, "what do you think our bedtime routine should be as the baby gets older?" Talking about some things further down the line will open the doors to communication and show that you are interested in coparenting fully without sounding like criticism of what she's doing now.

Some babies just need more holding and attention, and trust your wife's intuition on that. No baby was ever hurt by getting too much love and attention at 9 months!

Some suggestions on how you can help your exhausted wife... take over laundry duty and do it completely. This may take a week or two to tackle a little at a time at first, but then do one load a day and you'll find it's not a big deal to put it all away immediately - you can fold in front of the TV and put stuff away during commercials. No biggie. Same with the dishes. Just decide that you are going to tackle the kitchen each evening. Once they are done daily on a consistent basis, you should be able to get it done in 15 minutes or less for two adults and a baby. No big deal, again.

Don't pressure her to do more housework right now. Just do more yourself. I find that when one person in a household is doing more work, sometimes the other person will do more. However, your wife has her hands full right now and it's not the priority.

As for you helping more with the baby, keep in mind that children's preferences to be helped by or held by or talk to one parent over the other change as the child grows. There will be a time when you will be the only one your child wants to help her with her shoes or homework, and so on. And sometimes, the child gets the parent who is available to help at the moment, not necessarily the one they are screaming for!

If your wife is working as much as you say, the baby has plenty of time without her to learn to crawl and be out of her mother's arms. Don't worry about it. Let the relationship happen naturally.

I would strongly recommend that you read some parenting books by John Rosamund (or something like that) like Parent Power. It's more for when the child gets older, but it has been a life-saver in raising my child, and was a great starting point for a lot of discussions in our household about how we wanted to parent together. We both read it and then would talk about different parts of it informally.

You work, your wife works. Pitch in, and do what has to be done at home, and teach her by your example.