For your father's example it seems you haven't set up an Email Account for his domain in Outlook, i.e.
billwood@firstdriving.co.uk — he's just using his ISP address to answer any messages that arrive for 'First Driving' because I presume you forward them to his BT mailbox? If you create another Outlook email account for him (for the 'First Driving' domain), when creating or replying to a message in Outlook that has more than one account configured, you have an [Accounts] button next to the [Send] button and you use it to choose which account to send from, which will control how a reply-to message is addressed in the outgoing headers. The default outgoing address (if you forget to select one) will be the default email account set in Outlook, which is presumably the BT one? It's easy to change them around if that's what you require. Note: you may have to use the BT SMTP server for outgoing messages, rather than the domain mailserver — I'm not familiar enough with BT to know whether they block you using SMTP servers other than their own.
For the second example, I'm not sure if I misunderstood what you've written? By writing 'redirect' do you mean he has a Forwarder set to deliver all mail arriving at his domain to go to Yahoo? Anyway, providing your client uses Outlook to POP from and SMTP to Yahoo, all you have to do in Outlook's Menu is (and this is for Outlook 2003 but they're all fairly similar):
- Tools >
- Email Accounts... >
- Select [Radio Button] 'View or change existing email accounts', then click [Next] >
- Select the Mail Account name from the listing - by default Outlook would name it after the POP server, like pop3.ispmailserver.com but you may have renamed it, or you're using the mailserver associated with the domain you host? Anyway, click [Change...] >
- Click [More Settings...] >
- Select 'General' tab - the page contains the Mail Account name (which is where you'd find 'pop3.ispmailserver.com' (or whatever), then it has two other fields: 'Organization' and 'Reply-to Address' >
- Enter 'enquiries@indagatio.co.uk' in 'Reply-to Address' >
- Select [OK], [Next], [Finish] to complete the changes.
Every time his default mail account is used to create/send an email it will then set the Reply-to Address correctly in the mail headers.
If you don't want to set that Reply-to Address for every outgoing message, just ones that are pertinent to Indagatio, you can leave the Reply-to Address window blank and BEFORE SENDING, when you're in the Message Editor (the Outlook one, not Microsoft Word as the editor) go to the Menu > View > Options > Look for Delivery Options halfway down that window > Tick the 'Have replies sent to:" tickbox and type 'enquiries@indagatio.co.uk' in the adjacent window > [Close] > [Send].
I don't think you can do this automatically by creating a Rule for outgoing messages that match certain criteria, then have a Reply-to address set - certainly not with any of the default actions available.