My 15 & 17 old children work for our family LLC. Do I need to issue them a W4?

YES ... you need to file a W-2/W-3 and all required payroll tax forms needed so you can deduct the employee wages on your business return.  

ALL employees must receive a W-2.  In addition, there may be state requirements you must follow.  (For example, in New York state, the "payroll protection act" requires that employees must receive a pay stub or statement with 15 or more specified pieces of information, and failure to provide a statement that conforms the law is subject to a $100 fine per employee per pay statement.)  On the other hand, some requirements may be waived if you employee family under age 18, but you need to check your state laws.

You don't need to withhold social security and medicare tax from family under age 18, but you do have to treat them like real employees in most other ways, including issuing a W-2.