It sounds as if you are in a situation where you cannot work due to lack of childcare
availability and you therefore could have been furloughed
, but the employer is not obliged to furlough its staff. It is a matter to be agreed. Another alternative is to ask for time off (unpaid) for looking after a child.
There does not appear to be a redundancy
situation and therefore the termination, if on the grounds of lack of childcare in the current circumstances, would be grounds for unfair dismissal. Also, there is a possibility that the employer has breached the implied duty of trust and confidence in dismissing her in circumstances where she has refused to bring her child into work with her. However, if you have not been employed for two years you would not be able to bring that claim.
As for discrimination, there is a possibility of a claim for indirect discrimination on the grounds of sex, the argument being that more women than men have caring responsibilities for children and the provision, criterion or practice, of requiring all employees to come into work is more detrimental to her on grounds of her having childcare responsibilities.