They walk a fine line if they're asking about this in an interview, the only thing reason they might need to ask is to determine your ability to be there during the likely scheduled hours, in which case you only need explain that you have a child care arrangement and a back up plan in place. I wouldn't necessarily think you needed to advertise that you have children, but definitely don't conceal it. It is worth asking why they would need to know if they ask about it though...
It's illegal to discriminate against someone who has/doesn't have children, so they shouldn't even be asking the question.
If there's a gap in your resume you can legitamately fill in as Self-employed, then do so. Obviously add in the details and achievements.
If you have scheduling issues, then certainly bring that up, as there's no point lying and saying you can work X hours when you can't, but otherwise, it's none of their business.
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