Relay for Headlights & Park lights ?

You can only have output voltage to either 87 or 87a, not both. The way you suggest wiring the relay will have output to terminal 87. You'll need a second relay for the running lights.  

Technically, if you used a large amp relay, you could physically run the headlights and the running lights at the same time.

But what do you want to happen when you switch to high beams? The low beams should be switched off, unless you have four seperate headlight lens.  You would need some means of switching between the low beams and high beams, which is usually performed using the dimmer switch or a second relay.  By wiring the running lights and low beam headlights together on one relay, when the low beams switched off the running lights would go off too. 

Another downside to having both lights come on when the key is first turned on, is that the lights will be taking cranking power from the battery while competing with the starter.  Ideally, this would work better if you had a small time delay, say 5-6 seconds, between when you first turn the key on, until you could start the engine, then have the running lights and headlight relay activate.

Do your running lights come on now when your driving around during the day?  When you turn on the headlights with the headlight switch, do the running lights go out?  If so, you could tap into the running light line and have it activate a relay that would turn on the low beam headlights when the running lights are on.  Then when you turned on the headlights with the headlight switch, the low beams and high beam headlights would function normally.