It's very hard not to praise a child you love when they're pleasing you; I still do it, and I'm in my seventh decade and know better. So, empathy.
But your wife and you are right that praising the person - not the product or process - has negative outcomes. This has been studied extensively, especially in childhood education. In teaching, there's a saying: "Praise the process, not the person." (E.g. "That took a lot of effort on your part, and it paid off. Great work!")
When Parents' Praise Inflates, Children's Self-Esteem Deflates shows that there is, indeed, a lot of research on this topic.
In one paper on learning, 2 relatively small groups (N~300 each) were studied from 1st to 8th grade. One study was strictly about educational goals and isn't helpful in this case, but the second was:
In Study 2, perceived parent process praise was the only significant (positive) predictor of children’s learning goals, whereas perceived parent person criticism was the only significant (negative) predictor of incremental theories of intelligence. [emphasis mine]
When you make it person oriented as opposed to process, it doesn't help, and it may cause harm.
TL:DR: Motivation to try things can be affected by the type of praise a child receives (person or process.) Praising person hampers the motivation to work hard at tasks perceived to be difficult.
Many papers, including this one from 2013 have shown that person-praise leads to something called entity theory of intelligence, that is, the child believes that one's abilities are fixed, so if the child's perception is that they are likely to succeed at a task, they'll try, but if they think it's outside of their ability, they won't. This is opposed by the incremental theory of intelligence which assumes that abilities aren't fixed, but are instead malleable, and can be improved by effort and hard work. As a result, the child who thinks effort/hard work is the key to finding a solution is more likely to attack a task they perceive as difficult, since it's not about their ability, but about potential.
This research examined if mothers’ day-to-day praise of children’s success in school plays a role in children’s theory of intelligence and motivation.... mothers completed a 10-day daily interview in which they reported on their use of person (e.g., “You are smart”) and process (e.g., “You tried hard”) praise. ...The more person praise mothers used, the more children subsequently held an entity theory of intelligence and avoided challenge over and above their earlier functioning on these dimensions. [emphasis mine]
This page has lots of articles listed that examine the effects of person-praise in children as young as 1 year of age.
How can I address this situation?
If your mother respects research and (soft) science, show her the abundance (and it is abundant) of research about this subject. If you can convince your mom to keep most of her praise about process, then you can forgive the occasional slip up of person-praise.
Use google scholar for your searches, including key words such as "praise", "process", "parenting", "motivation", etc. You'll find plenty of support.
Edited to Add: It's not wrong to praise the person when they actually deserve the praise (e.g. you know your child is a kind person. "You're a very kind person. It's one of your many good qualities.") It's an observation, it allows your child to be seen and appreciated by you for who they are. What we're discussing in these answers is equating a child/toddler's value with pleasing us. That's not a very good thing.
My eldest child, now in his 30s, recently confessed to me that he still fears displeasing me, not because I react badly, but because it makes him feel bad about himself. This broke my heart; I want him to live the life he wants to live, and I love my all my kids unconditionally. My oldest was already beyond toddlerhood when the first study of this kind came out, but I did praise the process often; it seemed intuitive. I also praised the person. As Robert Burns said it best, "The best laid schemes o' Mice an' Men, Gang aft agley/ An' lea'e us nought but grief an' pain,
For promis'd joy!" We are damned if we do and damned if we don't, but it doesn't mean we should not try our very best.