In order to load the processor in the order you want, what you can do is to load the showconfig.aspx. From the showconfig, you will get the current order.

Let say for example, this is how it looks in showconfig

<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="Confirm"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="CheckTemplateLinks"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="CheckCloneLinks"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="CheckLinks"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="CheckLanguage"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="UncloneItems"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="Execute"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="PostAction"/>

And you want to load your processor between the Execute and PostAction. You just need to use the patch:before the PostAction. Something as below:

<sitecore>
  <processors>
    <uiDeleteItems>
      <processor mode="on" type="Custom.DeleteItems, Custom" method="RemoteDelete" patch:after="*[@method='PostAction']"/>
    </uiDeleteItems>
  </processors>
</sitecore>

Now, if you are on Sitecore 9, you can use the new feature which is the Configuration Layer. This allows you to load files in specific way. You can get more information from this blog

In order to load the processor in the order you want, what you can do is to load the showconfig.aspx. From the showconfig, you will get the current order.

Let say for example, this is how it looks in showconfig

<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="Confirm"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="CheckTemplateLinks"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="CheckCloneLinks"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="CheckLinks"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="CheckLanguage"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="UncloneItems"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="Execute"/>
<processor mode="on" type="Sitecore.Shell.Framework.Pipelines.DeleteItems,Sitecore.Kernel" method="PostAction"/>

And you want to load your processor between the Execute and PostAction. You just need to use the patch:before the PostAction. Something as below:

<sitecore>
  <processors>
    <uiDeleteItems>
      <processor mode="on" type="Custom.DeleteItems, Custom" method="RemoteDelete" patch:before="*[@method='PostAction']"/>
    </uiDeleteItems>
  </processors>
</sitecore>

Now, if you are on Sitecore 9, you can use the new feature which is the Configuration Layer. This allows you to load files in specific way. You can get more information from those articles:

1. Sitecore Documentation

2. Sitecore Configuration Layer