I think you really need to stop trying to please your mum. She mentioned the army so you thought you'd do that as it would please her. But you realised it's not what you wanted so you decided to do the uni course. Why you mum suddenly decided it's not a good idea even though she supported you at first I don't know. My mum is a bit like that too though, I've been firm though and not let her influence me any more.
It is her money, but as others have said, this is your life and you mum will be proud of you once she sees that you are happy in life. She's probably just worried that this course will get you nowhere and that you will end up unhappy and without any money.
While she will certainly have to pay for the first year now, since you haven't saved up any money yet, you still have the option of taking up part time work while you're at uni (which I'm going to do) and work in the holidays. You should be able to work hard in the next summer hols and save up a lot them for the second year.
But really just sit down and think about your options, what do you want to do? The army was not really your idea and so it didn't work out, you have to find something you really want to do, or it will be a waste of time.
If you really think this degree will get you the job you want, then go for it is my advice!