How can I prove residence in the UK when I had employment breaks such as periods of time involving childcare?

You can use many forms of acceptable evidence and you only need to provide proof for 6 months for each year, for 5 years in a row, to apply for settled status. The list of acceptable evidence is here and contains evidence such as bank statements and council tax bills:

https://www.gov.uk/guidance/eu-settlement-scheme-evidence-of-uk-residence


The Home Office also states that they are willing to work with individuals who may not have enough evidence in their own name suggesting that they may be willing to accept other forms of evidence. If you have lived in the UK for 5 continuous years, apply for settled status and submit additional evidence if needed. Although accepting pre-settled status may seem easier, pre-settled status is a limited leave to remain in the UK for 5 years and offers fewer rights than settled status.