From what you indicated, I would hold off on another pup for a bit.
First of all, I suspect that a lot of the issues are because you just moved. Bama needs time to feel secure in the new home.
When you say a playdate, do you mean other Havanese or all size dogs?
You might be putting too many things into Bama's life at once. I would let her get used to the new house. And when you walk by the neighbors house, keep your head up, look straight ahead, and keep walking at a great pace. She may be picking up that you might be nervous or apprehensive about the other dogs. If she sees that you are confident, she will pick up on that and maybe not feel the need to bark at the neighbors house.
A puppy or beginner obedience class might help her get more confidence so that she is more comfortable in her own skin.
Once she has begun to be comfortable in her new home, and be ok with the neighbors dogs, and has good manners (which she will teach the new pup), and is fully potty trained, then it might be a better time to bring a new dog home
I dont want you to feel I am discouraging you, but I would hate to see BAma take a HUGE step backwards because you have brought a new dog in, and are spending time with that dog, and she is just not ready.