The background details:

-Located in Tulsa, Oklahoma.
-1/5th acre size lots
-Neighborhood built in 2000.
-Wife bought the house in 2015

I have a question about flooding that is occurring in my backyard.  There is a very slight slope in the backyard that slopes from one side to another and from front to back(I have noted these in yellow but the slope is even across the whole yard.  This slope carries on to yards around us.  From what I can tell, the way the land was originally graded, the natural flow of water should be across the fence of the neighbor with the landscaping(noted in red) and either continue east across their yard.  The landscaping is mounded, blocks some of the water flow and causes it to pool in the corner of our backyard inside the fence, noted in blue.  The flooded area is usually 150 square feet and since our soil has lots of clay, it sits with standing water for days and days after a rain.  

My wife bought the house in 2015, prior to us meeting, and the issue existed when she bought it.  I looked though pictures on old listings and this landscaping in the neighbors yard existed when they bought the house in 2010.  However, it wasn't in place when their house was originally built.  We recently married and I want to get this taken care of.  

Since the backyard slopes away from the road, we can't drain out to the road in front.  My MIL was under the impression after speaking with the landscaping neighbor a year ago, that they would be ok with us hooking into their existing French drain system.  Supposedly the neighbor with the landscaping had mentioned to my MIL or wife that the previous owners had complained about the standing water after a rain or something along those lines.  The only way to do it completely on our property would be to have a sump pump installed over there to pump the water out to the road.  Obviously this isn't my top choice since we would need electric run to the area, sump area set up, pump cost, and ongoing maintenance.  

My wife contacted the neighbor wife earlier today about some upcoming fence work and mentioned that we would like to set up our French Drain system in conjunction with the fence work.  The neighbor now says that from a legal and house resale perspective, she doesn't think they'll let us hook up to their French drain system and said we should do an electric sump pump system.  I don't expect them to be neighborly about this issue and would anticipate them to tell us we're on our own.  

Legal questions

From my basic understanding, you have to let water flow across your property and if you change the topography that causes the water to back up on upslope properties, you are responsible.  This may be wrong but that was my impression.  

-Is my understanding of the legal aspects of this correct?

-Legally, do they have to fix this rainwater drainage issue (either by allowing us to hook in to their drain system, removing the landscaping, or some other way) or are we on our own?

-Do any of the other factors(how long its been since my wife bought the house, landscaping existed prior to them owning the house) effect this at all?

Here is a rough diagram showing what’s going on.  Up is north.  Yellow line shows the directions of slope of the yard.  Red is the landscaping, blue is the standing water area.   Attached File

Where does your "legal" impression come from, OK zone ordinance? What research have you done prior to asking for national opinion?

Is this a HOA neighborhood? If so document the changes and when. If not approved by the HOA you can have their landscape pulled as it's affecting your property.  Maybe when faced with that they'll reconsider letting you tie into their drain.

Surface run off is completely different than water ways or seasonal water level/swamp/wet lands.

As long as it's not their surface run off coming onto your property it's not their problem, it's your surface run off on your property it's your problem in my city.

Call your city's storm water or engineering dept and ask.
It's a common question.

Good luck

My neighbor called the city and filed a complaint about my land draining into his back yard.

City guy came out.  I told him the name of the well known developer that was responsible for the grading.

I also asked about his permit.  

Complaint went away, neighbor left with shit in both hands, clapping.  

Do your research.

Yeah, I ended up correcting it, but on my schedule, and at the developer's expense.  He needed to buy a drainage easement and it cost him $30000. He cut the check based on the name of the lawyer I chose.  

Before proceeding any further find out if there is a drainage easement across the yards.

Most states have statutes regarding water and water run-off. You can find that on line.