Let's say we have a good wooden door HP 15, Hardness 5, Break DC 18.
someone wants to open the door and another is pushing the door from the other side to remain close!
what's the dc open now?
do they have to make str checks?
what + or - do i give to each one of them?
To make it easy, I'd probably add the Strength mod of the character holding the door to the Break DC.
Hardness and HP aren't a factor unless you're trying to chop the door to bits with an axe (or some other destructive means to reduce that door to bits of broken wood), in which case, someone pushing it from the other side won't matter.
Break DC would be to break the lock, usually, or the hinges, so that you can push the (still intact) door open - once broken, the door would no longer be capable of remaining closed on its own, but it might still be swinging freely on its hinges. Someone pushing from the other side is aiding the lock to keep the door closed. So the Aid Another rule could be used here; each person pushing to keep the door closed could add +2 to the break DC.
+2 doesn't sound like a lot, but on a d20 it's not just 10%, it can be a huge difference. For example, a STR 8 weakling could, eventually, break down the door quoted by the OP, given enough time and enough tries (statistically, about 10). Add +2 from someone pushing back, and now that guy can never break the door down. Ever. That's a lot more than just a 10% difference. An average guy (STR 10) could break that door 3 tries out of 20, but if it's held, that drops to 1 try out of 20, that's a 66% reduction. Even a strong guy, STR 20, suffers a 17% reduction when the door gets that little +2 to the DC.
Once the attacker successfully breaks the door, now the door is not holding itself closed anymore, so this is just an opposed STR check, attacker trying to push the broken door out of the say, defender trying to prevent that.
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I agree with the above. It is clean and simple.
Now if I wanted to make it cinimatic (party holding the door to keep out a massive monster while the the cleric is healing the fighter) I would make it apposed strength checks. If no one beat the DC 18 break DC then the door would not move. If you defenders beat it and the aggressor did not then the door would not move. If both parties made the DC then it is a strait strength check. As at that point the door is no longer the issue. I would allow aids to either side as normal.
But that is just for the flavor and the thrill.
EDIT: by the above I mean adding the strength of the person holding the door.