How do I survive as a single mom with two little children and a very demanding job?
Pretend you’re “Dad”
First: remove the part where you're a mom.
Pretend you're “Dad”
Overall, society is far more supportive of men in the role of single parent. For women, we act like you're doing something wrong, somehow. By the way, you might want to think of yourself as a female Head of Household (which is your tax status, if you're in the US).
OK. Done that? We're pretending now we're talking about a widower who has two young children and a demanding job.
Now the problem has more obvious solutions:
Get domestic support
If you have a demanding job, hopefully you have one that allows you to have full time help. Yes, you will spend a lot of money on this, and that will lower your standard of living. But that's what you need to do.
If you are working yet not earning enough to hire anyone to help you, look for other work, get a raise, or if neither of those are feasible, you're going to need to recruit volunteers from among your friends. Depending on your kids' ages, you at least need someone to supervise them. Ideally they should keep your home clean too.
Beyond that you will need people on call for when your kids get sick, to take them to the doctor - that might be a close friend or family member, or it might be the same household helper.
You need to have backups for when your helper gets sick, has a personal emergency, or takes a vacation. No, you can't cover that yourself.
The advanced level of this is to have two people working regularly with your family so that there is always backup.
Simplify your life
Think in terms of household processes: food, cleaning, money management, transportation…. Make them as efficient as possible.
Have groceries delivered or find healthful meals to pick up... or get into a neighborhood meal rotation (each person cooks once per week for the group) if you haven't hired someone to cook. Hire a bookkeeper.
Anything that is an onerous chore that you don't enjoy doing, get rid of if you can. Remember, pretend you're a widower with two children - there is no guilt. Just get rid of those tasks. Do not take on any more tasks.
Avoid shopping and adding stuff to the household
Get rid of clutter. The only things you should be buying are utter necessities; your household is an investment, not — right now — an expression of your innermost design aesthetic. Don’t buy anything unless it improves processes. What you need more of is time and space, and you get that by hiring people to do work for you.
Take care of yourself
You need to stay healthy. Exercise regularly. Go to the doctor. Vitamin C helps you metabolize cortisol (stress hormone).
Be fully present with your kids
Remember that memories are made by repeating the same thing over and over. If you have the same pattern and activities with your kids, even if it's not all that frequent, they will remember it and be able to ritualize it, and it's that ritual that will help them feel your presence even when you're off working.
Develop a daily "check-in" habit. When my son was in preschool we did "What was the best part of your day? What was the worst part of your day?" That can take one minute or a half-hour. Have them leave you a picture and you can draw a picture back if they don't talk yet and it's hard to see them during the week. Even little things if done daily keep you in mind.
Keep a list of fun things that you can do together so you can pick something new without needing to plan it. (Or - I have seen people hire taskrabbits to plan them a fun outing, also - or if you have a friend who's good at this, ask them to suggest what you should do with your kids when you have time off.) Remember for little kids "the park" is a great outing.
Try to give your kids a picture of what your work looks like. Take a photo of it if you can't bring them there to see it themselves. It will make a difference to them to know where you go, and what you do there. Make sure there are visible reminders of them in your workspace when you bring them there, if that's possible.
You're probably going to need to train them for "I need a moment to unwind" and they need to wait. You do that by rewarding them if they can give you a moment with your full, undivided attention. (It's worth the training...). It's tough, because they can't really wait that long when they're two. But by the time they're in school they should be able to give you 20-30 minutes to collect yourself when you get home.
If you possibly can, try to also establish an individual ritual, maybe once per week, where you have time with one child when the other is busy doing something else (and vice versa).
Btw, notice I do not say to kill your career. Do not do that.
Also, you are allowed to date, even though your time with your children is scarce. But be careful not to introduce a dating partner to your kids too early, just because it's more efficient for you to be with them all at the same time.