I had this same problem, and it took some digging, as the Exchange Remote Connectivity tool error message is quite misleading.
What this turned out to be, for me, was a reference to a CAS server that had recently been removed, in the databases' RPCClientAccessServer property. (As a bit of background, Exchange is new in my environment, and I had set up Exchange with some 'test' hostnames. Once it was time to move to production hostnames, I removed the test servers from the environment...)
The RPCClientAccessServer seems to not be set dynamically. Obviously, as this is my initial Exchange implementation, I'm no expert, so if anyone can provide any more info on this, please indulge me.
Anyway, the resolution to this issue was as simple as grabbing the databases and resetting the RPCClientAccessServer property, using PowerShell.
For example, the following gets all databases on host "mailbox01", and sets the RPCClientAccessServer to "newCAS02":
Get-MailboxDatabase -Server mailbox01.example.local | Set-MailboxDatabase -RPCClientAccessServer newCAS02.example.local
Note that these should be FQDNs.
To give credit where credit is due, I found my solution here http://exchangeserverpro.com/outlook-clients-unable-to-connect-to-exchange-2010-after-client-access-server-role-moved
I thought I'd post it here, because it mentions nothing about the "EXCH provider section missing" error, and this solution was a little tough to track down.
is the "https://MS2010.MYDOMAIN.local" the URL you're trying to connect to externally? I could be reading your autodiscover wrong, but that's what I'm seeing. If so, that's probably your issue. You need to set your external domain in the outlook anywhere to match what your actual external OWA address is.
http://technet.microsoft.com/en-us/library/aa996902.aspx
See this command as an example:
set-OutlookAnywhere -Identity:'CAS01' -ExternalHostName:'site.contoso.com'
Actually, it might be helpful if you could share the following results of:
Get-outlookanywhere
Secondly, how is DNS setup? Can we get view of "mydomain.com"?
Do you have port 443 and 80 open on your firewall and pointing to your CAS server?
Does your firewall have a log that you can share?
Basically, if it's not working externally, I'm incline to think its one of the following:
DNS, your firewall or your external outlook anywhere configuration.
Best Answer
I managed to get this working by using NTLM authentication.
In the EMC I enabled this by going to Server Configuration ? Client Access and the properties of the mail server. Then on the outlook anywhere tab chose NTLM authentication as the method.
Then on outlook, in the account settings > more settings window > security tab I set Logon Network Security to NTLM and in the Connection tab > Exchange Proxy Settings chose NTLM authentication
And then it worked!