I've read a few different stories about that

Love to read yours when its done
So far Kagome had full blood demon pups for a few reasons:
- She has a high amount of power or miko's of high strength can have demon pups
- Kagome was able to carry demon pups because she carried the shikon no tama
- Kagome goes into heat like a demoness would
- Youkai find out some humans can have full demon pup's
- Kagome is mated at a certain time
- There is a witch or dark miko involved somehow
There are some more reasons too, but in all the best ones there is a good explanation which links in to either Kagome's past or events.
Hope this helps

I'll keep an eye out for the story