Make very very sure that changing the contour of your property does not affect your neighbors or your property when it comes to water drainage during a rain, heavy or otherwise.

On the left it's more of a sharper drop, in their garden. I was thinking of flattening more the garage side (right)

I think once you have a bigger patio you could make a feature of the slope rather than try to change it as that is a bigger job.
If it were me I would divide this garden into 3 areas, patio, lawn and Den/play area.
Some form of trellis/arch or even a bush/s across the lawn where the path turns to give the children a sort of secret den area in that bottom third? Children love the idea that you cannot see them and they dont mind about slopes so much. Also the perspective of the arch/trellis could really change the look down the garden from the house.
If the washing line was nearer the house it would be out of the childrens way and easier for you to collapse down or even put away more often.
Good luck and please show us what you decided to do.

Thank you Drc762,

I had thought about a very small raised bed along side path and then drop the grass.

I like the den area at back.