Hi Kami,
no, not madness - go for it! :-) It's obviously something you really want to do.
I did something similar, I started a PhD about 15 years ago and left half-way through (after 3 years, I was doing it part-time) for a number of reasons: supervisor problems, having a baby, being very fed up with it... I am now almost half-way through another PhD (full-time and fully funded this time) in a completely different subject are. I'm really enjoying it. :-) Just one note of caution: my last experience has had quite a negative effect on me and led to (or at least contributed to) major depression. It also really undermined my confidence which is still affecting me now: I constantly feel I'm not good enough and can't imagine actually completing this PhD, even though, objectively, I'm doing ok. You might not have the same issues, of course, but just be aware that your last experience might affect how you feel about doing another PhD.
Good luck with it! :-)