The APA style has a few settings in it that can cause the issues you describe.
Please see the following KB on how to ensure that the initials do not appear for the in-text citations.
You may also want to look at the setting “Add more authors until the citation is unique”
In EndNote you can go to Edit > Output Styles > Open Style Manager > locate the style you are using > Click Edit > go to Ambiguous Citations under Citations > here uncheck the box Add more authors until the citation is unique > go To File > Save As > (EndNote will not allow you to change the existing style in EndNote but will always apply the change to a copy of the style) Click Save to save the changes to a copy of the style > close the style window.
Please feel free to contact Technical Support directly if you need additional help with editing the style.
1-800-336-4474 option 4 then 1