For young moms, I think the main challenge isn't homeschooling itself, but how to do it all and keep toddlers entertained without feeling you've somehow neglected them. The following are tips I have given to moms in this particular state.
1) Your number one goal in raising your children and in homeschooling is to educate for eternity. Our God given task is to get our children, our spouses, and ourselves to heaven. If we happen to learn Calculus along the way, that is a bonus. Remind yourself daily that is is why you are homeschooling. Begin everyday with prayer and some kind of devotion. It doesn't need to be complicated, we often read about the Saint of the Day or the Mass readings for the day as our devotion.
2) You cannot do it all. You are not and should not be expected to do it all. Obviously something needs to give. For us, what gives, is a perfectly cleaned house. On any given day we really could not have guests just pop in without their seeing just a little bit of chaos somewhere in this house. It took me years to let go of a perfectly clean house, but let's face it moms, we have children, sometimes many children at home ALL THE TIME, whereas our public/private school moms have many, most or all of their children out of the house a good portion of the day.
3) Let go of perfect. From an early age, I began teaching the children to do many of the household tasks. There is a learning curve and I had to let go of perfect. Take a deep breath, let it go.
4) Do not be embarrassed, ashamed, afraid to ask for help. Help can come in many forms. If family is available they might take your non-school age children for an hour of two a week so that you can homeschool your school aged children. Other homeschooled families may have teens seeking service hours or a little income. A good friend who was trying to keep her head above water hired our oldest daughter to come a couple times a week to help out. Sometimes she played with the preschooler and toddler, but more often she helped homeschool my friend's oldest daughter, allowing my friend to play with her younger children, or get some much needed housework done. If you can afford it, having someone come in and clean bathrooms and mop the floors once a month can be a huge help.
5) Keeping toddlers and preschoolers entertained can be a real challenge. While babes in arms can be worn in slings, nursed, or nap during school, toddlers tend to be into everything and require nearly constant activity and supervision. This is so incredibly difficult while trying to teach phonics or addition. If you are like we were, having about a two year space between each child, you have a near constant stream of toddlers disrupting school. Strategies that have worked for us have included: schooling during morning naps, having older children take shifts playing with a toddler, and using short videos (Veggie Tales and Signing Time work very well and left me nearly guilt free for having implemented them as a distraction for my toddlers). By the time our toddlers were about 2 1/2 they really did want to be included in our activities. I have a special box of educational toys just for school hours. Our little ones would sit at the table and play with these toys for almost long enough for me to help the older children with their school work. This year our three year old sits through our science and history lessons. This has been such a blessing. They really can absorb so much information just by listening. He could tell you all about glaciers, volcanos, and the twins Romulus and Remus.
6) This tip I discovered only once I had a high schooler. Nothing counts until you hit high school. Prior to high school your educational goals should be relatively simple: by the end of second grade your child should be reading independently and able to read instructions for their school work. Independence is a huge goal, worthy of striving for in your homeschool. By junior high you will need to focus on introducing your students to higher scientific concepts and emphasize writing skills, preparing them for high school and beyond. Therefore, if you find yourself absolutely swamped, minimizing homeschool in the lower grades will not be detrimental to their overall education. In lower elementary, formal math and reading are all you really need to focus on. Choose science, history, art, and music that need only be done occasionally. Capitalize on your children's interests and read, read, read and explore, explore, explore.
Over our 12 years of homeschooling, we have implemented nearly all of these tips. We have survived. We have more than survived, we have flourished.
I know these tips don't even come close to being exhaustive. If you are an experienced homeschooling mom, please feel free to leave your valuable tips in the combox.