How to improve this query performance by indexing properly?
Since you have a foreign key from CHILDEVENTS to CHILDINFORMATION and you don't select any column from the child information table, you can skip that table. One less join will certainly not hurt:

SELECT CHE.CHILDID, COUNT(*) AS CURRENTWEEKPOTTYBREAKS        
FROM  BKA.CHILDEVENTS AS CHE           
WHERE CHE.TYPE ='POTTYBREAK'        
  AND CHE.ADDDATE BETWEEN @currentweekstart AND @currentweekend         
GROUP BY CHE.CHILDID ;


As for indexing, the existing index on (Adddate,Type) INCLUDE (ChildId, EventId) does not look very good for this query. I would try replacing it (in fact removing both those AddDate-Type indexes) with an index on:

(Type, AddDate) INCLUDE (ChildId)