I would do this, not by poking around and digging, but by taking the entire plant out of the pot and slicing off with a big knife, a section of roots with sucker attached. that way the disruption is minimised to both the big and little tree. Then put the big tree back in the pot with a good
compost mix in the empty section and it should be fine. I might wait another month or so until the tree is growing quite strongly, being an evergreen.