@Youseethethingis:
The mom is doing all of the heavy lifting. She has to do all of weekday tasks, chores, school activities. During the week that my kids are here, we have school, homework, medical appts , music lessons, and when it was not curtailed by the pandemic, we had sports and cheer practice after school. During that time we still managed to go out for dinner and have time during the week to have a family movie night.
So , it is a bit presumptuous to assume that the mom is not actively involved in social activities with her children.
The dad only has them for 28.7% of the week while the mom has them approximately 71% of the week. It is not the mom's responsibility to manage or negotiate her ex's social life or down town, and the mom is spending considerably more time managing and maintaining her children's life and activities than the father is doing.
The mom does not send her children to the OP. She sends her children to spend less than a third of their week with their father. If the father is passing his obligations on to his partner that conversation should require no mention of the mom.
The OP is asking her partner to give her some down time. The OP is not a child who needs to request permission to take time that she needs for herself. Perhaps her partner treats her like a child over whom he has control because she presents herself as a child who needs his permission.
The OP will liberate herself when she assumes control of her own time and actions.
You never need permission to control that which belongs to you, and her time certainly belongs to her.
OP start acting like an adult, and perhaps he will respect you as an adult. If not , leave him to manage his children on his time .