Even though she is your mother I think you are being far too good to her.
You don't have a four bedroom house where she can sleep, you have a one bedroom flat, and that is meant for 1 or 2 adults, not 3.
You also have a baby on the way so you need all the space (and peace) you can get a the moment.
Having her living there, even if she was the nicest person in the world, would be difficult, but if she drinks, and gambles and has other problems it must be awful. Even worse she borrows money of you.
I am afraid you seem a bit of a soft touch. You need to get MUCH tougher.
Tell her she has a certain time to move out (a month say).
Tell her she has to pay towards the rent/food while she is there.
I also agree with cloverjo, I cant believe she would get nothing out of her marriage that failed.
Did they not own a house? Is the husband still living there? If so, and there are no other children living there, she can force the sale of this house and get half the money (or get her ex husband to buy her out of her half).
I know it may tough telling your mother she has to move out of your flat, but you have to do it for the sake of your boyfriend and upcoming child. Your mother has to learn to stand on her own two feet.
GET TOUGHER. Or your mother will sponge off you forever.