I sympathize. I identify! Indeed, the Grouchy Mama Society is worldwide!
After all, you're doing two (or more) full-time jobs, so frustration comes with the territory. When we're tired enough, we even fall into the trap of embracing our grouchiness. Yuck! So, without wanting to put any more burdens on you, I encourage you to start with yourself.
How tired are you? I bet the answer is VERY. You're working all day and - with a two-month-old - all night.
Are you a perfectionist? Do you yearn for things at home and in your work to be so good that no one would complain or criticize about them? Do you feel guilty a lot?
Achieving a balance is hard. You can take some small steps toward that goal, but you'll need some patience with yourself.
If you haven't had a checkup lately, you might want to get one, just to make sure nothing is physically wrong with you other than fatigue.
Husbands are sometimes good helpers at home and sometimes not. Anyhow, they have their own work to do. But if you can hire some household assistance for a while, it would be a great investment! Call your local high school; a reliable student who could come a couple of afternoons after school could take a bit of the load off your shoulders until both you and the baby are sleeping better. Hire someone who is really efficient at vacuuming, bathroom-cleaning, ironing and other housework. This will free a little time for two other priorities: resting yourself and playing (remember playing?) with your little ones.
This is a good time for you to streamline your day as much as you can. Can you unclutter your home to any extent? Ask your six-year-old to help you! If you're a perfectionist, decide to lower your standards temporarily, making your home clean and organized enough to live in even though not everything is done well all the time. If there's a way you can streamline your paying job, too, figure out how.
Children tend to be frustrated when Mama is frustrated. Not that they won't disobey, fight, or whine the rest of the time, but when Mom is tied up in knots the kids seem to get worse. So starting with your own chaos is a way to help theirs.
Oh, and start looking for things to smile at right now! It sounds silly, but it's crucial. No matter how overwhelming things are, find something that lifts your spirits - three or more times a day. Make it a treasure hunt of sorts, because you'll have to search! Discover even tiny things that make you smile or laugh. What's outside your window right now? What expressions are on your beloved children's faces?