1.) Another method to check if the point lies on curve entity is to check for existence of parameter value, or distance value with (vlax-curve-getparamatpoint curve GivenPoint) or (vlax-curve-getdistatpoint curve GivenPoint)... "curve" variable is 'ENAME of requested polyline...
2.) You can try to retrieve DXF data of list that is before newly added vertex when you use (vla-addvertex) method and construct new polyline with (entmakex) and also retrieve DXF data of list that is after newly added vertex and construct second polyline also using (entmakex) function with which you can also get their 'ENAMEs at the same time...