Yes, many homeschooling parents will say you should. It's helpful for children to witness a parent, or both parents, working - whether that be working in service to the greater good or community, or working on their own dreams. I've spent some time in the past not working and entertaining and educating the kids without any work interruptions at all. After some time, not only did I feel frustrated to not have any time to myself to stretch my brain and have a wider-community sense of purpose and achievement, but I also started putting my needs for work-outcomes upon my kids, where I put too much pressure on them to work with me on homeschooling projects without recognising their personal needs. Also, I had a deep sense of lack in meeting one of my values of homeschooling, which is to help educate children of the real world and how they play a part, belong and contribute, instead of having them live in a bubble until graduating traditional school at 17/18 years of age.
Homeschooling has the bonus opportunity of children being in the real world observing what adult life "after childhood" will look like. It's a great privilege for them to witness us parents in a working state of being, regularly. It helps them cast out a vision of their own, which shapes their personality and passions at a young age, giving more meaning to their play and social life.
Recognising the benefits of working from home, it's also important to recognise that it can also become hazardous if the homeschooling parent's time is dictated by other people outside of the home. I've learned the hard way to not take appointments or have other people waiting for me to be on a phone call, or in a meeting, or at a certain place, at a particular date and time especially if exchange of money is involved. I've found it both stressful and unproductive to try to live a double-life of a "normal" career as well as homeschooling. Homeschooling really does require you to embrace it, love it, and shape other aspects of life around it.
Any freelance work is ideal, of course, being that you will be working from home, in your own time. If you can manage your own time, and work on projects that are "outcome focused" rather than paid on labour alone, that will work well.
A job or contract that requires you to work a certain number of hours per week, and to clock in and clock out, will often be unsuitable, unless you have a partner (other homeschooling parent) with a flexible schedule that can wrap around your shifts.
You can choose from many vocations, such as product distribution (either holding the stock yourself, or network marketing where the company holds the stock), where you create a website, e-commerce system, customer service program, and social media marketing plan.
You can work as an office assistant for a local business, such as a local tradesman or small business that doesn't have an office or business premise and is looking for someone to use their home-based office and computer.
Family day-care can work if your children are all under 6 years of age.
Writing a blog with affiliate marketing advertising can provide an income if you tap into a genuine target market and offer a real practical solution to an popular everyday problem, and you know how to create a solid reputation and social media presence where people can get to know you, like you and trust you.
Graphic design is an excellent vocation for part-time working homeschooling parents and pays well, as does marketing, branding, and logo design (supplying business marketing material) but beware that this is a higher responsibility to deliver excellent quality work to a client who is waiting and has a deadline - so will really depend on your personal situation.
You might also consider a cooking or food business such as delivering fresh bread, eggs or produce, a plant nursery, a tutoring or coaching business that can be done mostly by email correspondence, video editing, illustrating, sewing, landscape photography, all the way through to becoming a registered BAS Agent or professional report writer.
Just an FYI - A vocation that I've personally found challenging is recording youtube content, or providing virtual holistic wellness sessions or training videos such as yoga or meditation, because when young homeschooling children are in the background making all sorts of surprising sounds, the audio quality is just not professional and continual distractions may not be not fair to impose on a good paying client unless discussed beforehand.
Learn how to meditate independently in your own time and benefit from better health PLUS enjoy teaching your children how to meditate for enjoyment.