How old is the child going to be? You mention infant and under 2. If the child is truly an infant (up to 9 to 12 months) I would just do him/her on your lap. With the cabin pressurization they are going to be doing a lot of holding and calming the baby anyway. Now if you are talking closer to that 2 year old age I would definitely do a separate seat as a 1 1/2 to 2 year old will get heavy by the end of 2 hours.
Now as
@dreamfinder mentioned there is no reserved seats on SW but when traveling with small children you do get to board right after priority boarding, prior to general boarding. So there should be no issues with most of everybody sitting in the same area. At the very least your brother-in-laws family will be together