Be very careful about appearing to have divided 'loyalties' or divided 'commitments'. Some managers are inclined to view mothers in the workplace as liabilities or employees who will let them down and don't need much encouragement for their minds to wander in this direction.
Some companies have a culture in which total and complete commitment of a 24/7 nature from employees in terms of emotional and psychological engagement with work is seen as necessary.
In light of this:
The 1:1 is scheduled. I work for an organisation which prides itself on a ‘holistic whole person work life balance’ approach. We have to assess ourselves monthly on how we feel we are at work, in the team, in our role, healthwise.
...please do not use the "I've sorted it but it wasn't easy" line.
Your organisation is one that holds its employees in suspicion. The built-in, regular reflections on how things are going are not meant as an opportunity for someone like you to share details of your family life, your ups and downs, your challenges.
What you are supposed to do in these sessions, what they expect from you, is reiterations of your loyalty to the company and your dogged determination never to let your actual life interfere with your commitment to its bottom line or to deliver to clients what the company expects.
I fear you have misinterpreted the function of these little sessions and believe them to be safe spaces to share - they are not. They are set up to monitor your engagement with the company, with your role, and your level of willingness to prioritise your work above everything else.
I urge you to please watch your back, because a tendency to appear as if you are finding it hard to cope with all the demands on your time and energy will be used against you.
I would say 'Sorted of course' in response to any question about dealing with what family life throws at you, and look bemused at the question.