I would square it with the property line. Find out what your side and rear set backs are, and then work within that area.

Squaring it to the house may limit the pool size because of set backs.

Your plan to cut down the dead trees down will take away from that defined line you speak of.

If you put a fence on the property you'll be back to square one. Sweeping, free from planting beds though along the fence, will soften things up and break up the rigid line.

Thing is, you'll really only notice these concerns looking at a plan view of the proposed work. It will be hardly noticeable from a ground level vantage point.

A 3D rendering from the contractor, if they have that capability, will give you a better idea how all will look before the work begins especially a "fly through" aspect.

Thanks for your response. My gut says to square it with property line as well. I hope we can blend things together with creative landscaping and patio/deck. I keep looking for decks that are on a diagonal and not parallel with the back of the home.

View looking straight from the back of house and view from deck looking straight into back yard

Does it have to be a rectangular pool? I'd look into a freeform style so that it's not square with anything.

A free form pool would definitely solve the problem, but we like swimming laps and the kids like to race back and forth. Plus the free form pools are a more than we’d like to spend on a pool.