Should I leave a treeline to mitigate flooding in my backyard?
Poison ivy

To get rid of the poison ivy, 1-2x/year spray all the (undesired) broadleaf ground cover in the area with 2,4-D herbicide according to instructions.  2,4-D only harms broadleaf plants, so overspray won't hurt your lawn. It won't hurt established trees (unless you use way too much).  It is a very old, trusted and well-proven herbicide that hasn't had troubles like Roundup has. Buy it pre-diluted (pink) not farm-grade (deep, opaque crimson) because the latter is strong enough acid to blind you.  keep it away from areas you plan to garden/eat becuase organic is better :) 

Flood water

This question can only be answered with a deep understanding of the lay of the land.  This is engineering - not particularly hard engineering, well within the reach of a serious "jack of all trades" - but it answers the question so conclusively that it's the only science you need on the subject.   

Note that "swift moving water" type floods, like you get on hillsides, are very different in nature than "water slowly rising" type floods like you see in Houston or the Mississippi River valley, and I assume you are talking about the latter.  

Water will very reliably seek level.  So if you know the comparative altitudes of each part of your property, you can predict where the water will go at different flood stages. Very likely the city has that information.  The insurance company also clearly has some data, or they wouldn't have written flood insurance, and you wouldnt have gotten a mortgage. 

The number you will typically see on maps is "feet above mean sea level".  And a contour map will show lines across the property, each lone is at a certain altitude.  Suppose you have a 25' contour line at the base of your property, and if you're lucky the map has them every 1'.  There'll be a 26' contour line a few feet up your yard, then a 27' line, etc. etc. 

If water rises to 25', everything below the 25' contour line will be flooded.  If it rises to 26', then the area between the 25' and 26' lines get flooded.  Etc.  

If you can get a contour map and look at it, then walk around your property,  it will make a lot more sense.  So talk to City Hall or your county GIS department, i.e. The guys who do the tax maps, and see if they'll print you one out for a few bucks.