OP I think you're going to have a difficult time with this one. I've known many parents whose own parents ( the young children's grandparents) offered or in some cases insisted to provide full time care for infants and/or toddlers. In those cases the grandparents were well off financially and did not want to paid for their help. I am a nanny and I have personally worked with FOUR different families who were looking to replace a grandparent as full time caregiver. One of those families had a ten month old with a broken leg -- grandma fell down the stairs while carrying him. The second family's two year old suffered a broken arm at the playground while grandma "was taking a break on a bench on the other side of the playground." The third family thankfully had no injuries, but the mom was getting frustrated that grandma wasn't following her instructions, and had been feeding her 22 month old Oreos and kool aid regularly (the mom was sending a lunchbox with healthy food and wondered why it was never touched) and also let her watch "way too much tv." The mom said she "still has no idea how much tv" her toddler was watching, but "she knows all the characters from doc mcstuffins, caillou, Mickey mouse clubhouse, and more and we don't allow tv at home." The fourth family is my current family, they also had issues with grandma spoiling DS with sweets and tv. But they had two bigger issues: Grandma never enforced any rules or boundaries, and they've had a LOT of behavior issues in their son (now 2 years old), and also, grandma was often asking for days off with little to no notice. I'm told asking for a day off once per week with less than 48 hours notice was the norm, but the final straw was when she asked on a Friday afternoon to take the following Monday through Thursday off to visit a friend in another state.
I also often see the same grandmas at the local playground with their grandchildren. There are two of them, and they look so so tired every time. They each have two grandchildren to care for, one has an infant and a 3 year old, the other has a one year old and a four year old. They are both always sitting down on the benches, chatting, the baby is with them but the three other children are running around the playground. The older kids are always yelling "grandma come here! Come see me! Come play!" But their grandmas never budge. The one year old has, more than once, gotten into trouble (going too high up, getting stuck, trying to slide down the fire pole which is not safe for her it's very high up and she can't even really reach it but still tries) and I have had to be the one to help her because it seems if I don't she will fall down 6+ feet. I wonder what happens when I'm not there.
And those grandparents all work on a voluntary basis! When you factor in money and employing your mom, it gets A LOT more complicated. If you pay her too little, she might get upset when she speaks with nannies nearby who make a lot more. If you pay her a competitive rate, then you're still paying as much as you would for a true professional nanny who will have had a lot more recent experience, will be more up to date on current child rearing standards (no spanking, on their backs to sleep, tummy time, no screen time for under 2.5, is she current in CPR for kids, etc), will be more likely to follow your instructions and treat it professionally (not take advantage of excessive time off, etc), and will be more likely to be physically up to things like wearing her in a baby carrier, or chasing her all over the playground, etc. And it's hard, even as a nanny who really likes my nanny family and knows they treat me pretty well, not to feel a little resentment towards them once in a while, for things like leaving dirty dishes in the sink or asking me to stay late, etc.
The last thing to consider is something I've seen repeated on the DCUM non nanny forums a few times: Don't hire a nanny you can't fire. If the arrangement starts to go south, you're going to have such an unbelievably hard time telling your mom, dealing with hurt feelings, and even more resentment.
If you really want to go down this road, something you might consider is having your mom be a part time nanny (1-2 days per week) and find another nanny part time (3-4 days per week). That would help your mom be less burned out, and if you do need to transition to a different nanny full time it will soften the blow a little and you'd already have another trusted nanny your child is familiar with. Good luck.