Sorry to hear that your husband has overlooked all of the major positive things that you're doing, and has chosen to focus on what appears to be relatively minor negative things. Given your post, here are some of my thoughts...
We have two children, 5 years old and 3 months old. I ... decided that I would start a business instead of returning to work so that I could have the flexibility to take care of the kids during the week with all of the practices, doctors appointments, school stuff and whatnot.
Your rationale for flexibility is a good one, but starting a business just for this seems premature, given your situation. How much "school stuff" and "practices" do you have with a 5-yr old and a 3-mo old? I would imagine next to none.
Did you discuss starting the business with your husband before quitting your job and taking out loans for business expenses? What were his expectations regarding your business, in terms of your weekly commitment-level, contributions to finances, etc?
So here I am trying to get this business off the ground meeting with contractors, vendors, negotiating leases, buying supplies, etc. to start this business since the baby was 4 weeks old. I am still waking up with her at least once a night and am often so stressed about everything that I can't sleep so I am pretty exhausted.
Here's the thing. I do all of the housework and childcare as well. Drop of and pick up son from school, laundry, dishes, homework, dinner every night because my husband is a workout freak, bills, cleaning I do it all. And I work my ass off trying to make everything perfect. I have no free time for hobbies, exercise, or anything other than a 20 minute shower at the end of the day (if I'm lucky)
For just a moment, let me play devil's advocate. Along the lines of the previous question, how have you met your husband's expectations of contributions to the household finances? For all of the time you put into your business in addition to these chores, is it profitable?
This is a key piece of information. If your business is not profitable, your husband likely credits your time spent doing business-related work as a hobby versus actual work. Making the same assumption, if your husband is the sole breadwinner, it's a natural (and reasonable) expectation that the spouse not contributing to the household income helps out more around the house.
Whatever your situation and that of your business, it seems like your husband should be more involved when it comes to the division of labor, and more appreciative of all that you do.
Today I had laundry out on the couch that hadn't been put away. My husband went off on me saying that I can't keep up with everything, I don't know how to manage my time, that I'm dirty and I used to be so meticulous about the house...
I'm super crushed. I try so so hard. This isn't the first time we've had this argument and his logic is always the same "you stay at home so you can do the housework." I can't change his thinking and it kills me that he doesn't see how hard I try.
It's inevitable that if one spouse spends more time in the house and has more flexibility in his/her day job, the spouse working outside the house sets these expectations. I work from home, and face this issue with my wife, who works at a hospital and sometimes has very early starts. She frequently assumes I can do a greater share of household chores, am available to run her errands at any point during the day (e.g. carting her to work, bringing her lunch, going to the post office or DMV). In the end, I feel my wife's expectations are unfair, so I feel your pain.
I would hail back to the expectations established with your husband when your business was getting off the ground. Remind him of the time commitment, what was agreed, and that you're treating this as real work, so he should respect your time in the home office as the same.
he wants his mother to come stay with us a couple of nights a week to help (she doesn't speak English or drive so obviously it makes me a little uncomfortable).
I think this could be more trouble than it's worth. Is there any reason your husband might feel a need to help her (is she in need of a place to stay, something else)?
I am tired of feeling unappreciated and ... I want to leave... but I just signed a 3 year lease for this business space. I've spent money to get it running. I quit my job. I don't want to split up my family because my kids love their father. I feel so stuck and hopeless.
Stay to keep the family together or because you think there's hope for your husband, not because of the business lease. Try not to let factors like this affect your decision-making.
In general, if you've brought children into this world, you must weigh the certain, adverse effects on them over their future from a divorce, versus the potentially uncertain benefits you (and perhaps they) would reap from moving on.
I would recommend marriage counseling before divorce. I feel unappreciated by my wife just about every week, and I don't believe that alone is good grounds for dissolving a marriage. Good luck!