First of all, this Covid pandemic is very scary to a lot of people. As for this MIL, from what you shared she has three children and a young 7 year old and she can't afford to get sick and possibly get very sick. It's also very possible the mother has abandonment issues too given that her husband left her and used his legal skills to escape being financially responsible to his wife and children.

As an outsider you can see things that are probably unhealthy. However, even though you would like to fix what you are seeing, you really can't fix another person or a family that has unhealthy dynamics. Your girlfriend already knows that talking to her mother and her grandmother is useless too. And your girlfriend more than likely is at the age where she needs to get away from them from time to time too. At 21 years old an individual begins to want to engage in finding themselves away from the family unit too. With this Covid pandemic taking place, that has put a considerable damper on distancing in a normal way.

While someone at age 21 can seem mature in many ways, they are not that mature and still don't have their true own identity either yet. What you feel is playing hard to get probably isn't a game but more of your girlfriend being cautious and not wanting to make her homelife even more challenging than it already is.

It also may be that your girlfriend, though wanting to fly free and even find distance from her family, may not be ready to commit to a long term relationship right now either. It's actually best for anyone to learn how to be independent instead of going from one dependancy situation to another one. A person goes through a lot of changes in their twenties. Once someone graduates from college and begins to learn how to work they learn a lot about themselves. Also, there is a subconscious knowledge in your girlfriend how important it is to be independent, after all she watched her own mother have to learn how to do that in order to care for her children. Your girlfriend also felt the affects of what it means to be abandoned due to her father not only walking away but also taking steps to reduce his financial responsiblity to his own children. She lived with the aftermath and how it affected her siblings and herself. And because of that she is most likely unsettled subconsciously which includes deep emotions that even she herself may not know how to understand.

What is love, what is having a healthy relationship with a man even, never really seen it or lived to watch it in her parents. These are things she simply doesn't know. Hard to get? Perhaps that not really what this means even though you feel that's what it is.