@mummy917 Hopefully the texts about your mum have ended but if he starts them up again tell him to text your mum not you, this is between the two of them. They are both adults, and whether it was appropriate or not, you are not his whipping boy and he can't berate you for someone else's actions.
Regards the extra shifts and childcare. If you are receiving UC then you need to be aware that working the extra shifts could place you in a precarious financial position and perhaps you should consider your wellbeing during this period.
If you pay extra for the nursery on a Friday UC will contribute to that costs and that means that you are not asking for financial recompense for the whole day cost from your Ex and may choose to absorb it yourself if it suits you.
Even though you are supposed to be 50/50 you are still carrying a lot of the mental load for this shared care and you do this for your children and it may reduce as time progresses. Meanwhile you are doing amazing, there are no instructions on how to navigate this rollercoaster.
Be kind to yourself picking up extra shifts may distract you, however they may not be as beneficial financially or mentally while you are juggling this change,