How to combine these two queries and have them be as fast?
Would help if you post SHOW CREATE TABLE for the two tables and also how many rows each table has.

Most likely the slowness is due to use of LIKE "%Smith,John%". This will do a full table scan on tbl_employee.

Try LIKE "Smith,John%" just to see if the query performance is any better this way. I am assuming you have an index on tbl_employee.name column.