Did you read the FAQ that I linked to in my first post?
Any membership "allows" MMS messages to be sent but MMS messages are not covered by any membership or separately purchased add-on allwoances - they must be paid for from cash credit on your account (30c each).
Hope this helps.
I still don't know why you're having these problems and would be inclined to blame the usual Apple stupidity (e.g. with iMessage?) that causes problems for end users.
To be fair I doubt that you need to change your phone over this and it should be possible to get things working.