Practice, practice, practice. It might be that you have a slight hearing impairment, or perfect pitch, or something else that's making it harder, but people who really can't hold a tune at all are extremely rare. It soundsto me as if this is more to do with the fact that making music is relatively new to you.

I also love the idea of learning another instrument - I hope that's helping! If you don't want to sing where other people can hear you, but you're not sure of tuning when you're on your own, you can learn a lot by singing along with recordings. As someone has already said, the main task is to co-ordinate your ear with your vocal equipment, and it sounds as if you're well on your way there - it's just a long process.