Skyline Honey Locust trees are a wide spreading tree (35 feet) providing filtered shade.  They should not require any pruning when young.  As they mature pruning in late winter can be useful to lift the canopy so that you can walk beneath it.  Their wide branching fast growth (up to 50 feet) should be a good choice to shade your house.  But it will be light shade not heavy shade.  Do not plant it closer than 20 feet to the house.  The following websites show a mature tree along with growth requirements.

1. 
https://extension.usu.edu/botanicalcenter/trees-of-varga-arboretum/skyline-honeylocust

2. https://www.chicagobotanic.org/plantinfo/tree_alternatives/skyliner_honeylocust

Should it bifurcate like the second photo to increase its spread.  How does one prune a tree for bifurcation?  Tanjs!

There were no photos attached so I can’t visualize what your tree currently looks like.  If you are trying to change the leader to split into a two leader I would not advise that.  It would make for a weak connection that could split the trunk at a later time and destroy the tree.  This is naturally a wide spreading tree.  If you do not like the structure of the tree as shown in the above websites, it would be better to choose another tree.