Your question is confusing because the title doesn't really reflect the question body. It reads like your Min Pin already accepted the new one and they are in fact forming a pack. You didn't mention any growling or biting or fights, which is a great sign.
The other behaviors you list are part of this current process of forming a pack. I see 2 categories of actions:
Playful: the play bow is a quite sure sign of playful behavior. The low growling and nipping could be part of a play, but they could also be signs f aggression. Those are very easy to confuse and I would have to see your dogs in action to be sure.
Dominating: the herding, mounting the other dog and putting the head on his back is clearly dominant behavior. What you perceive as "running away" is actually a natural answer to this behavior. If the second dog would answer with the same kind of dominance, they would probably end up fighting. The second dog avoids a real fight by giving way to the first dog.
Now in my honest oppinion, you should let them figure out their ranking in the pack on their own, withing reason. That means:
- Don't interrupt every instance of dominant behavior. That leaves them both with unresolved issues, which could easily cause tensions in the near future.
- Do interrupt dominant behavior that has been going on for too long. If the new guy doesn't get any rest because he's constantly herded around the house, put an end to it. If the Min Pin keeps the new guy from eating, drinking or defecating, stop him.
- Do interrupt aggressions. Observe how the new dog react to certain behaviors from the first one to estimate what is mutual play and what is one-sided aggression. If, for example, the first dog starts nipping or growling, the second dog avoids this behavior by turning away or trying to walk away, but the first dog doesn't stop, thats aggression. If the first one starts nipping and the second nips back, that's probably play.
And the most important advice that many people get wrong: accept their own rules! It's already clear that your dogs have a clear ranking. You should accept that ranking and neither treat them absolutely equally, nor pity the new dog and treat him better.
- Feed the higher ranking dog first! Not observing this rule can lead to fights. If the low ranking dog needs more time to eat or special food that you don't want the high ranking one to steal, feed them in seperate rooms.
- This includes treats. If you give the same command to both dogs, give the higher ranking one his treat first.
- Don't make the high ranking dog wait or stay before an open door while you let the lower ranking dog walk through. Just like with food, this is a previlege of the dominant dog. By artificially changing it, you make the low ranking dog challenge the dominance of the other one.
- If there is a high and a low seat for both dogs, let the high ranking dog claim the higher seat. This may seam insignificant to us today, but it's just as ingrained into our subconciousness as it is in dog's. Just a few hundred years ago the throne of a king would not only be the highest chair in the room, it would be the only chair standing on dais to raise it above every other chair.
In addition to that, accept that they are still individuals. I'm not a fan of only providing a single dog bed for two dogs. In addition to the big shared bed, they should each have their own bed in their own pen and be able to retreat to their pen at all times. Make sure that their pen stays the private place of each dog. The dominant dog must not be allowed to claim the pen of the submissive dog for himself.
And lastly, you are part of the pack! Your dogs are making progress, but if they never get any attention from you, they will eventually ignore you or exclude you from their pack. Maybe some of your problems arose because the Min Pin is bored because he cannot get attention from you? Start interacting with them again, do obedience training with them and play or cuddle with them. You don't want to be excluded from the pack and they don't want you to ignore them.