It's not easy to post everything that I've done and I'm not 100% sure this will work with your Ajax module as I don't have any running on child apps but.this is an old trick I learned a long time ago with .NET. Part of the problem with .NET is that child sites automatically inherit from the web.config in the directory above it (this may have changed as of .NET 3.5, I'm not sure).
Anyways, what I've basically done is when I launch a child site and it errors out trying to load something from the DNN parent site I've edited the child web.config to remove that instance. For example <httpModules> isn't used so I do the following.
<httpModules>
<remove name="Compression"/>
<remove name="RequestFilter"/>
<remove name="UrlRewrite"/>
<remove name="Exception"/>
<remove name="UsersOnline"/>
<remove name="DNNMembership"/>
<remove name="Personalization"/>
<remove name="ScriptModule"/>
<remove name="Analytics"/>
<remove name="Authentication"/>
</httpModules>
In your case I suspect that it's web extensions giving you grief so I'd try removing them.
<assemblies>
<remove assembly="Microsoft.VisualBasic, Version=8.0.0.0, Culture=neutral, PublicKeyToken=B03F5F7F11D50A3A"/>
<remove assembly="System.DirectoryServices, Version=2.0.0.0, Culture=neutral, PublicKeyToken=B03F5F7F11D50A3A"/>
<remove assembly="System.Design, Version=2.0.0.0, Culture=neutral, PublicKeyToken=B03F5F7F11D50A3A"/>
<remove assembly="System.Management, Version=2.0.0.0, Culture=neutral, PublicKeyToken=B03F5F7F11D50A3A"/>
<remove assembly="System.Web.Extensions, Version=1.0.61025.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35"/>
</assemblies>
I hope this might help.