Bougainvillea hybrid with deciduous broad leaf tree

[polaris]

Hi all .. we purchased this bougainvillea from a nursery a few years ago. Over the years it has changed it's character with a central trunk and branches emerging distinct. These branches flower with pink flowers in spring, then leaves come out but they die off by fall.
The bougainvillea stalks start from the base of this tree in late spring. However they become a bit ungainly and then my wife trims the bougainvillea branches completely .. in fact she prefers the tree with it's bare branches from fall through spring

My questions .. what is this tree that I have and what should I be doing about the bougainvillea branches that come every late spring.

Thanks
Bob

Photos attached
Base of the tree showing bougainvillea branches
Leaves of the tree

 

[cpp gardener]

Your "tree" is not a Bougainvillea. It is an Eastern Redbud Cercis canadensis. The shoots that come from the bottom ARE Bougainvillea. A seed must have sprouted in the Bougainvillea and has taken over. Choose one to keep and remove the one you don't want.