Dog people, advice needed

[rootbeerfloat]

My parents recently got a new puppy, O. They had an older dog (that passed away) who largely ignored the kids, but occasionally allowed them to pet her. DD was fine with the older dog, but is scared of O. Based on my limited experience, O is mellow and not intimidating, but she is still a puppy and wants to play. And for whatever reason, O really wants to play with/chase DD. At our last couple of visits, DD avoided the dog, made us carry her, and screamed bloody murder when O tried to chase her (and of course, her running just caused O to run even more). We will encounter this dog every other week or so, and neither my patience nor my back can sustain accommodating DD's fear for long.

How do I get DD comfortable with O?

[redheadbaker]

How well-trained is the dog? Maybe some calm petting while the dog sits still or lies down?

Could it just be fear of the unfamiliar? DS loves our dogs, but is terrified of everyone else's. But we don't go over often enough for him to get used to them.

[Jalapeñomel]

Can the dog be in a room or closed off area so you can easy into it or get away when need be?

[rootbeerfloat]

I appreciate the suggestions so far. Aside from supervised petting, are there strategies I can implement with DD to reduce her fear? Or is the solution just time?

[kangaroo11]

@ojo has great suggestions. I make the dog lay down so my cousin's kids could pet her without the dog licking/trying to jump on them. It helped a little and reminds the dog of her place in the pack (the bottom rung!).