Hi, 

With the Elm trees root growing up and intertwining with the poplar, it may be best to remove the tree all together as it will be really difficult (impossible?) to be able to dig enough of the root system to relocate it. 

You could do an internet search on how to take a cutting from it and try to root a new tree. Generally Elm are not the easiest to grow from cuttings and you would probably need some rooting hormone.

It could potentially be a non-native Elm too. Chinese elms are not considered invasive in the state of Maryland, however it can freely seed and is considered a 'weed tree' from US Forest Service . Elm trees are fairly difficult to tell the species when they are young.

Let us know if you have further questions about this. 

Emily 

https://www.invasive.org/weedcd/pdfs/wow/chinese-elm.pdf

sorry forgot to send the link about Chinese Elm for reference.