Day 16 is pretty late for a breeding. Normally dogs are fertile between days 9-14. That is why running a progesterone test is useful. It can pinpoint just when the dog will ovulate making sure the sperm is there when the timing is right.
www.woodhavenlabs.com/dogbreeding.html
If she is a hermaphrodite and her male parts were internal and out of view they would have likely been in the area the tube was inserted into and he'd not have been able to do that easily or normally.
You can read about hermaphrodites in dogs here
http://www.petplace.com/dogs/hermaphrodite-and-pseudohermaphrodite-in-dogs/page1.aspx
just scroll down for the full article.
They don't usually come in heat at all even if they look female if they have this problem.
I think on the first breeding your timing was off and that the dog may have developed an infection causing the bleeding.
Females sometimes will not stand for a particular male. Either they want a different male they know or they can tell that the male is not compatible with them for puppy production. This can be based on pheromones.
When I was young a free breeding female would be seen from time to time with a pack of attending males. The females always seemed particular about which male would get to breed them and it wasn't always the biggest or best fighter. Maybe your female chi knows more than you might think about mate selection. You might want to try a course of antibiotics for her prior to her next heat, a progesterone test when she is next in season, and a different male. I know I have always had the best success in breedings where the dogs were in complete agreement on the mating.
But perhaps this was not something that ended the pregnancy just an unexpected spotting.
You can run a relaxin test on her if she is past 22 days and see if she shows as pregnant.
www.bullwrinkle.com/ShoppingPages/ dog-pregnancy-test-canine.htm
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