I am American-born and I had several long-term friendships with people from Vietnam when I lived in California. Not that everyone is the same, of course, but I already see some similarities in your story and description to what I have personally observed.
Make no mistake, this middle-aged 38 year old woman has other boyfriends and love interests in the US and she is playing the field to get as much as she can possibly get--be that love, affection, attention, perks, contacts, job connections, funds for her family, or whatever it is she is after. It is unlikely that she has a plan or plot to marry you to get a green-card.
It is possible that she has a husband and children back home too.
Vietnamese people I've known, and all their friends, who have come to live in the USA have all had very similar behaviors to those you have described. They all tended to have numerous secret relationships who聽 they receive cell phone calls from and will at first reveal as "just a friend". Then next week say something like-- "his mother wants me to marry him but I don't like him that way" or something similar. Lots and lots of emotional games.
She is playing him (the one on the phone) and telling him that you are "just a friend." There is something dishonest and yet perhaps socially acceptable about this type of behavior or "playing the field" and not making a quick choice to get involved.
If she is away from her family, then she may be lonely and it may be quite reasonable for her to spend time with others and to then define her relationships with each in a way that will keep them --that is,聽 she will tell you whatever they want to hear to meet your expectations.
She knows you like her so she says that you are her "boyfriend". But what does that really mean? If you were living in a distant land you might do the same thing, out of need--for whatever it is she needs. If you were living in Japan, for instance, you would date and say things to please. Think about it. Have you ever lived in another country?聽 (When I lived in Japan I had to go along with certain social expectations without having any deep emotional connection to those behaviors).
Your "girlfriend" does not have the social obligations of an adult American living in this country since birth. She has less connection to society here and few deep social obligations. Simply put, she may be saying what she needs to say to keep the interest of any and all men interested in her.聽 And why not? She has strong connections and feelings to her family back home and will do and say whatever she needs to benefit them.
You know nothing about her and you cannot check on and verify or confirm what she tells you. She knows that and uses it to her advantage.
It is highly unlikely that she told her mother about you. That's just a harsh truth. Why would she? She says that to flatter you and make you think that she is serious about your relationship.
She is likely playing you to get some advantage. Does she need a job? Does she need connections for herself and family members? Yes, of course she does--now and in the future.
She might like you but she is playing all of her options with other guys too.聽 You can be sure that she easily hides the photos of the two of you together.
In the USA we would say that she is "stringing you along."
It's a certain style of emotional dishonestly that I have observed in great detail over years knowing transplanted people from Vietnamese living in the US. Also, I lived in a couple of Asian countries for a total of 4 years and it is quite common for men of high economic standing to have two families in different countries. Not all do this, but many do. It's an economic status.
A woman can do this too. Think about it. Your "girlfriend"聽 may have a husband and children in Vietnam yet she is economically able to travel to the USA. (You have no way of knowing how that came about. Did her family send her here to elevate them economically? Is she under pressure to do so by any means--that is play men? So maybe she just wants to expand her economic possibilities in the US. It could be summed up as simply as that.聽 She plans to return to Vietnam. DO you really want to get emotionally involved in that situation? Do you want to support her relatives in Vietnam economically in some way, either knowingly or unknowingly?
You can't believe what she tells you. The only way you will find out any truth about her is if you hire a private investigator--a good one--to follow her and get photos and to investigate her life in Vietnam. Do you want to spend money on that?
It's a very complex psychology you are dealing with--and you should start seeing other women. Don't get serious with this one. If she is seeing other men--and I can assure you that she is--then you need to start seeing other women. Don't fool yourself that you are in an exclusive relationship--you are not.
A "shy" 38 year old? Come on. Get real. More likely that she is not very comfortable for some reason--and learned to say "shy" to cover, or that you are interpreting her behavior as shyness. What might be making her react in a standoffish way that she then calls "shy"? Perhaps she's never cheated on her husband before with a non-Vietnamese man? Perhaps she only responds to Vietnamese men? Or maybe she just slept with someone else the night before? Do a reality check. Are you seeing her behavior as exotic when it is just dishonest?
It may be a learning experience, but you are also already caught in a tangled web and are trying to explain away her behavior even when you would not put up with it from anyone else! Of course she wouldn't have gotten up and left you to talk to a male friend. She was afraid her 'boyfriend" on the phone would overhear her "boyfriend" that is, you--that she was on a date with at the time. She knows that you are not in a committed relationship with either of you and that neither of you have any right to say anything about her phone conversations. You can't tell her who she can or cannot talk to. She's 38 years old! She is much smarter than you seem to give her credit for.
