Hi Ellie20
I would like to join our
resident wolf in welcoming you here

What are the main BPD traits you see in your mother? What would you say are your mother's most difficult or unsettling behaviors?
Right now I'm looking for tips on how to improve my relationship with my mother (communication tips, coping strategies, etc) and also how to ensure that she can have a healthy, positive and safe relationship with my baby daughter (who she loves dearly and watches frequently).
Turkish has pointed you to a great communication technique. There are also other techniques described on this site, the crucial thing in all of them is that we focus on our own behavior and responses. We cannot change or control what the other person does, but we can work on our own behavior.
Setting and enforcing/defending boundaries is also a very important tool often discussed on this site in relation to dealing with BPD family-members. Boundaries are primarily aimed at ourselves and keeping ourselves safe and healthy. Do you generally feel comfortable setting (and enforcing/defending) boundaries with people? Do you feel comfortable setting boundaries with your mother?
I am glad you joined our site
The Board Parrot