Is this mom over possessive?

My brother-in-law and his girlfriend announced she was pregnant last June. they had lived together for almost 2 years but they weren't very affectionate. I remember at Thanksgiving that she would not lift anything over 5 pounds even though her pregnancy was going perfectly normal. She found excuses not to come to our house (we live with my mother in law and her mother) when he would visit for Christmas.

She had a baby girl by an uneventful cesarean in January. After bringing the baby home she announces that they are not going to leave the house (except for doctor's visits) with the baby for 3 months. We find out that she took the baby to her aunt's house before 3 months, but wouldn't bring her here when we asked them to do the same.

She was nursing the baby but never produced enough milk and has had to supplement. No matter what the baby "has" to nurse to fall asleep. On mother's day she reportedly spent the entire day in the baby's room. she at first wanted my mother in law to baby sit then it was only at their house. Mother in law said she would be more comfortable watching the baby here since there are 4 adults in this house. she says "no thanks, my aunt will keep her."

when they all visit she constantly holds the baby. if any one else gets to hold her she would scream till her mom got her back. The end of this July, brother in law takes a job out of state with encouragement from girlfriend. he comes home about once every 2 weeks and she has everything taken care of as far as the baby goes.

they come over this afternoon, the first time in 2 months, (they only live about 20 minutes drive away). the baby is sleepy so, remembering visiting family frequently when my kids were that age, i made the bed in our room and laid a clean blanket over it and offered her to go in and close the door, nurse the baby and let her sleep for awhile if she wants.

she holds the (now 8 month old) baby while eating her dinner then promptly tells my brother in law that "we need to go" because the baby's sleepy and "if she falls asleep now then wake her later she won't go back to sleep later. we just have to go."

This has really upset my husband's mother especially since their father passed away suddenly last year. we don't know if we should address this, which will certainly cause my brother in law to be very defensive, or just let it go on.