Hi,
This sounds like the iPhone and Text Forwarding is almost treating the two Mac user Account like two different computers.
It also sounds like it can only be paired with one.
So after a bit of to-ing and fro-ing you have the User Account paired with the iPhone.
However the Mac end still seems to not send SMS messages.
An SMS sent messages should appear in green (like all the Buddy List accounts also do)
iMessages should appear as sent in blue Bubbles (I much preferred it when you could chose the colour you Sent with).
If you are choosing a Contact that does not have an iPhone you cannot chose an email (potential Apple ID) to send to them.
It has to be the phone number they have.
You may need to make sure their phone number is inclusive of the Country or region code.
Also check the iMessages Account Detail Button (you will need to sign in here as well)
Check the Country Region setting here as well as this can cause issues with plain iMessages to iPhone Numbers.
Check the Contacts app is set up to work for your Country /Region (Preferences > General > Address Format)
If the System Preferences > Date and Time > Time Zone setting is wrong it normally stops Messages even logging in.
9:30 pm Thursday; October 30, 2014
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad