My Pekinese nailed the neighbor's Chow. Should I get half of the $ for the puppies?

No.   Stud owner gets NOTHING unless there is a stud contract.  Owner of the mother owns the litter.   Owner of the mother assumes all the risks and costs of pregnancy, whelping and raising a litter..  there often is NO money after all the expenses.

Even at that, stud owners don't get half.    A typical stud agreement is ONE puppy, or cash value of one puppy.

These are MUTT puppies and will have no value anyways.

No, and I haven't heard the word "nail" in the past 20 years.   Otherwise, ask Mommy and Daddy about your concern.  https://au.answers.yahoo.com/question/index?qid=20210211234335AAncgzV

No but if push comes to shove, YOU could be entitled to receive stud fees from the owner of the b itch.   Good luck with that!!  And considering this is a mistake/mutt breeding, whereas in the past the stud fee used to be the cost of one puppy, these puppies won't be worth much over $50. each. 

Any puppies from this unplanned mating, will belong to the person who owns the dam of the puppies.

Nope. In fact if your dog entered their yard, they could sir you for damages 

It's Pekingese, you moron.   The breed is from China.

I'll bet you don't know how to pronounce it correctly either. 

No.  You have nothing coming cause it was an accident.  If it were planned, you would have gotten either the stud fee or pick of the litter.  If there is no contract you are not entitled anything.  A contract makes all the difference in the world.

To figure out how much to sell the pups for, the owner of the Chow needs to keep track of all expenses for this pregnancy & when the pups are 8 weeks old & ready to sell, she would add up ALL the expenses & divide by the number of pups.  There is no profit in dog breeding.  Vet bills would be the most costly.  So if she spent a thousand dollars on the mama & her pups & there were just 4 pups, they would sell for about $500.  If there aren't any Vet bills, the mama is being abused by not getting all the Vet work needed.  If all she spent was on food then there isn't much money to divide & the pups could sell for about $25 dollars each.  Keep track of all expenses.  So she can at least get that money back.  No profit in dog breeding.