First, congrats! You have a normal and healthy situation. We're practicing "Attachment Parenting" which you can look up on the internet and this is exactly what you would WANT at that age. Most experts feel it is critical that around 3-4 months the baby is strongly "attached" and bonded with the primary caregiver. Although is creates this stranger anxiety for now, later it results in more confident and well-adjusted toddlers and children. Think about it, would you want your 4 month old to just be happy with anyone? After all the time and hard work you've put in!!!
Also, I've heard about the horrible situation in the Russian orphanages where the babies have not attached to anyone. They will cling to ANY person that picks them up and cry for hours if that person (stranger) leaves.
So, although it's frustrating (and hard to deal with) for you and your Mom, have patience. I agree with Sherbet, to try and get a routine. Insist your Mom or any caregiver do their best to follow that routine. Children of all ages CRAVE predictability, routines and limitations. Have your Mom take over for a day, while you're there and do your best to not step in.
Also, is there any way you could do a part-time job? This has worked so well for our family and I was the primary earner before I went part-time. Yes, we have made MAJOR lifestyle changes and budgeting. I now clip coupons and worry about every penny, when I used to make solid 6 figures. But, it is so, so worth it.