I don't think it's an issue of 'read' emails being hidden, but you can check
that setting by going to View, Current View. That setting is saved separately
for each mail folder.
It seems you are talking about two different problems:
1) When you send a message, a copy is not put in your Sent Items folder.
2) Your MIL is not able to send or receive any emails on her computer.
You really can't mix up two different problems on two different computers.
Let's stick to one issue at a time.
What happens when she sends an email to herself? Does a copy go into her
Sent Items folder, and after a while is that message received in the inbox?
Are there any error messages?
Which antivirus is she running? Some of them cause problems with
Windows Mail over time.