I have seen this time and time again with SAHMs returning to work and Dh/DPs not wanting to do housework. Basically expecting the now working female to do everything they did whilst not working whilst also holding down a new job. FFS.
How it worked for us. Whoever is in the house tries to get a much stuff done as possible whilst looking after and seeing to the needs of the children. We are a team working toward a goal - downtime in which we can do whatever we want.
Free time needs to be equal, if you are part time and the children are at school then you need to be doing as much as possible. But also when he walks in through the door he is also on duty, just as you were when you no doubt picked the children up from school.
Because I was a sahm even when the children were at school I had a full schedule for housework, meal planning, batch cooking etc. Bins were emptied on set days so no waiting to notice when a bin is full. Dh loves cooking so I would do all the weekdays, term time and holidays, he would do weekends. Shopping was delivered as that takes time to do.
We tagged teamed so if one person needed a break they got it because it was reciprocated. Dh also took a child with him on tip runs, to the shops etc so he got one on one time with each child and I got one on one time with the other. Depending on the ages of the children they too can do chores, a toddler can put their clothes into a laundry basket and tidy up toys. Start it young, add more stuff in. 4 year olds can clear their plate from the table, clean and dry the table. It doesn't all have to fall to a parent. Everyone is on the team, and the team makes sure the house is clean and tidy.