Is it unstable and unfit to move 4 places in 4 months with a baby. She is extremely well taken care of. A lot has been going on

There is no simple answer to your question. When looking at the stability of a parent or the stability of an environment for a child to be raised in, each particular case is fact sensitive. I am not sure what your mother means when she says that your daughter will get taken from you if you choose to move again. There is no hard and fast rule that says if you live in X amount of places in a certain time period your are unstable or unfit. If DCS were to get involved, your constant moving may play a role in a decision that they make. Or if Father were to file a motion to modify custody, then this may be one factor that a Court were to look at when deciding where to place the child, essentially where are the best interests of the child most accurately represented. But absent one of these particular situations, there is nothing that can happen if you continue to move. My best advice would be to stop the constant moving and work on getting yourself in a stable environment where your child can grow and flourish. Do keep in mind that were you live and who you live with could be used in a custody determination hearing. So choose wisely and for your daughter's sake get some stability in her life.