I think it can be done. I've done it alone with a 3 and 6 year old and with dh home working full time at a job with a 5 and an 8 year old.
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Here are some guidelines we've learned to follow:
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Follow a loose schedule. Kids will start following it on their own once it becomes routine but if something doesn't go exactly as planned, don't panic.
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Try to have a schedule for yourself too as far as household chores
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Require a quiet time of an hour an a half or so a day. It isn't bad for kids to learn to work puzzles or read books or color quietly in their room(s).
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Try to return all phone calls during quiet time or when another adult is at home to watch the kids if possible.
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School time is school time; don't let anything interrupt this time.
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You don't have time for TV (ever).
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Your business/job is your hobby/entertainment
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lunches- make them simple and have a plan; leftovers from dinner are great; I know hot dogs are kind of icky but they heat in the microwave easy. Pre-make pizzas that you can stick in the oven. Sandwiches (goes great with a "picnic" in the yard).
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 Your kids come first. If someone has to go to the bathroom, needs a drink or snack, etc get up and do it right then no matter what you are doing. Show them they matter and rather than being spoiled they will trust you.Â
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Invest in a smart phone; answering e-mails on the go when the kids are occupied by something safe saves a lot of time when you finally do get to sit down at the computer.
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Are there things that are worth it to outsource in your household? I purchase a menu mailer currently and that has saved me from planning menus, wondering what I'm going to fix, driving to a restaurant and wasting my money, etc. Maybe you need someone to clean your house?
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In a pinch, young teenage homeschool girls can make great mother's helpers; a movie could be used occasionally (but not more than a couple of times a week) if you need some extra time to get caught up.
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Listen to your kids needs; Even with dh at home, my kids can not handle allowing him to do school and handle the bulk of the day so I have them from the time they get up until 6pm while he work. At 6pm, they are some how magically ok with me working and play quietly. At 7:30pm I stop working long enough to remind them to take a shower and supervise clean up (which at 8 and 5, they can do; not so much at 2 and 5 :) ).Once they are showered and cleaned up; I am lucky enough to have a husband who reads to one while I read to the other and then they are in bed! I work during the bath (because I can at their ages) and for 2-3 hours after they go to bed. This works at this stage. I may suddenly have to change this later.
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When mine were the ages yours were, we had school from 9am-11am. I did allow them to watch a little TV until 9am and would sometimes work during this time depending but it was turned off for the day at 9am.  At 11am we went outside and many times I did take a laptop to do some monotonous work but not always. At noon I served an easy lunch that required a couple of minutes in the microwave at the most and then by 12:45 they were off to their rooms for "quiet" time which usually turned into naps as long as they were in separate rooms. Occasionally my 3 year old chose to take her nap in my office on one of those kiddie couches that fold out.  I worked as I could when they were entertained by their dad in the evenings (I assume you will probably have parties a lot of evenings).
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Sadly, I do not have time to read great books, knit, or do any of those other lovely things that I hear other homeschool moms speak of but I am at home with my children and taking care of my family and that's what's important. I love my job though and I think that's what makes the difference.