I'm not sure if I am understanding you, but it sounds like you are running into the garden variety of race that always wants to **** slightly until you get it fully started - and even somewhat as is goes in.
When it cocks slightly, you need to be hitting the side that is NOT beginning to seat. A 2x4 over the side that is not entering the bore is needed. Hitting the tool on center only makes it worse.
You don't want the easy side to go into the bore much, before you attack the less cooperative side with full force. once started, it can still **** a bit and tapping sides - with protection between hammer and the metal race is needed.
If you have a grinder, you can remove some material from the outer
circumference of the old race(so it doesn't get stuck) and use it as the driving tool which can be hit directly with a hammer and wood for a more driving.
Again, all of this may be covered.
Good luck!