In App Designer the label handles are created in conjunction with, but separately from the main object. The handles for the labels are not shown in the Component Browser panel by default, but you can right-click on any of the items in the that panel to bring up an incontext menu that allows you to show/include those label handles in the browser.
Then it becomes are simple as you are currently doing to change the visibility for the slider.
function ctrl_check_chkValueChanged(app, event)
sldr = app.ctrl_sldrOfIntrest;
sldr.Visible = 'on';
app.("your label handle").Visible = "on";
sldr.Visible = 'off';
app.("your label handle").Visible = "off";