Sounds like maybe the code for INT0 isn't releasing the microcontroller (infinite loop?) or is changing something needed by INT1. I know that isn't much help, you probably already knew that.

So to debug:
my favorite method of debugging may not be what other people would suggest but it is something I have learned from C++ programming...i.e., pop something on the screen saying "you have made it this far". For example, print out a 00 at the beginning of INT1 and a 01 at the end of INT0 or something. I like having visual clues that my program is at least getting through code and not hanging up because it is easy to get stuck in an infinite loop.

Another method that I use is the oscilloscope (my best friend). If you are using the clock line on INT1, echo the data line on another line (p1.0 or whatever line you have available). If you are able to see an echo of the data AFTER INT0 has done its thing, then you can move forward from there and keep debugging.

Hope this helps!