I could be completely off track but I don't think OP is being completely straight with us. She does not answer any questions about whether she has family. She provides no information about how she met her partner.
I get the impression that if we knew the full story, we would judge her.
So this is my take:
OP, aged 22 and pharma uni graduate, went into this arrangement with her eyes open.
She was dazzled by the 14k per month and the lifestyle of not having to work, despite the slightly creepy aspect of him being 19 years old than her and almost twice her age. Her graduate friends who could not find jobs were envious.
Her parent(s), with life experience behind them, did not approve of the age gap or relationship. OP does not want to go back to living with them or seek their support hat in hand because they would say I told you so, dispelling the image of the perfect life she has from the outside.
The circumstances in which she met her dp are somewhat questionable. Either it was a sugar daddy arrangement (he financed her uni degree) or it was an affair which broke up his first marriage/family/relationship.
At the time, she felt she got the Grand Prize because she 'won' him over another woman.
Then as she had her first child, she realised he did not do any parenting or housework other than pay the bills. Their roles divided strictly on gendered lines.
But that did not bother her all that much because that was the deal. They had another baby.
Over time, the cracks started to form and get bigger. Two children were more work than one. She did not have any spending money or free time of her own.
However, something happened recently which required her to change the entire calculus of her choices.
Perhaps another younger and less encumbered woman has caught his eye. The writing is on the wall.
That opened her eyes as to how vulnerable her position were to be if he traded up and how she could guard against it.
Hence her OP.
It was not about how to make him do more housework. It was how she can get out of an economic and financial arrangement of convenience that was running out of road.
If you got this far, hope you enjoyed my flights of imagination.