Just hang in there, and give your daughter as much time as you can under the circumstances. Both you and your daughter are lucky to have your mother to help you out. Right now your daughter may be more attached to your mother than she is to you, although at 4 months the attachment process is just getting under way. But if she sees you, is sometimes fed by you, spends time with you, gets comfort from you, she will also attach to you.
As you have only one day off each week, you probably want and need to do other things during that precious time. However, I would urge you to spend as much of that day taking care of your daughter as you can. Even though you might just want to lie around the house with your feet up, do as much for and with your daughter as possible. Remember that rest is change; whenever you do something different, you are resting from your major task. And, if possible, give your mother the day off and hopefully even have her out of the house for part of the day. Being the occasional “Mother of the Day” will help you eventually become “Mother of her Life.”
One other suggestion, and an important one: choose a name for your mother (grandma, mimi, mamoo—whatever is used in your family) and say it frequently to your baby. Point to her and say, “Where’s _________?” And just as frequently call yourself “Mommy” to her—“Oh, you and Mommy are going for a walk.” Although your daughter is much too young to say either word, she will begin to associate the two words correctly with the two of you and separate your roles in her emerging mind.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.