If you ask people who the greatest guitar player in the world was, you would get varied results, but someone would inevitably say that it was Jimi Hendrix. Even if you disagree about Jimmy Hendrix being the best, you have to admit that he was very good. Jimi Hendrix taught himself how to play guitar.
I think training at home is fine but I have to agree that your relationship may present a problem. That aside, there are some right ways and wrong ways to go about it. First off, you have to decide what the two of you want out of the Martial Arts. Is it for self defense, to learn the art, sport, or for the experience of the dojo.? If it is either of the last two then, training at home is not for you. If it is to learn the art or self defense, then training at home may be an option.
The key things to remember for self training are:
- Curriculum - Know what you want to achieve and design your program around it.
- Schedule - Set time aside for training and stick to it.
- Accountability - Have someone that is going to encourage you to stick to it.
- Seminars are your friend
As far as accountability goes, I would not try to self train with lessfewer than three people. So in your situation you need to find at least one other student. To be clear, self training is not the optimal way to learn martial arts. Youtube and DVDs are a great source, but a good teacher is worth their weight in gold. Home training should really be a supplement, not a replacement for formal training.
Look here for a couple of articles that cover "Deciding to Self Train" and "How to Self Train"