Exactly which DID chain are you working with mate ? Is it a 50 NZ, DS, DZ, do you know ?
The following applies solely to DID chains. I happen to work for the UK importer and so can speak of this brand with certainty. Other brands may be similar but I am not gonna hold my hand up and say they are the same .....
There are only two types of clip links used on DID chains: RJ and FJ links.
The difference is that FJ links,(usually only used on 420 and 428 pitch) have side-plates that will push on with fingers and can come off just as easily.
The type of link is usually indicated on the packet (if it's in one)
RJ type clip links are known as press-links, they have a a friction fit side plate. They require the side plate to be squeezed on to to the link with pliers or similar. It will fit then securely and will need taking off with either a grinder or a chain splitter, you will not get it back off with fingers.
The Horseshoe clip is fitted as an extra security measure on both types of link. The closed end should always face the direction of chain rotation.
I would guess you have an RJ type link and you have a problem where the side plate just sits on the edge of the link, not sliding on fully ? That is how it should be.
Use a pair of mole grips (or whatever you guys call em over the pond) to gently squeeze it into place and fit the horseshoe clip on afterwards so the closed end faces the direction of rotation..dont squeeze the side plate on too tight though or you will have a frozen link or tight spot in the chain. It needs to be on just far enough to allow the horseshoe clip to go on.
Incidentally, if you have sealed ring DID chain links, never, ever hammer the end of the links over to peen the ends flat.
They
must be flared over using the correct type of chain tool. Hammering the pins over causes micro-fractures in the hardened chain pin and can lead to catastrophic failure of the chain. Many moons ago, DID chains did need hammering, but the manufacturing method and construction was changed ages back. It seems though that many members of the general public and even some dealers are still not fully aware of that fact.
take care out there