All I can do is make sure the know we are there for them when their mother is flaky and give them the stability they don't get from her
Ok so how do you propose you do that when you see them EOW? A few hours a month simply isn't enough to give them stability.
She is awful
Yet you're happy to have two beautiful innocent children living with her and be neglected whilst pretending that the children aren't neglected when they don't get medical treatment, have their needs met or basic hygiene.
I wish she would be less shit together and be less crap
You've said yourself she's unable to and you are unwilling and unable to help her. When are you both going to accept that she is not going to get her shit together or be less crap? Will it be when the children are 18?
I want her to be more considerate to them, and to me, and my child.
So it is about you and your child then because you have said several times she isn't grateful to you, has not treated you well and she's not considerate of you.
She isn't grateful to have her own children, she doesn't treat them well and she's not considerate of them. If she can't do it for her own flesh and blood, how on earth do you think she's able to do it for you? You, your wants and your needs are so so far from her mind, can't you see that?
They shouldn't move in with us, we will not take custody of them.
So bottom line is you aren't really there them at all, are you? Neither is their father. No one stepping up for these children.
So much disapproval and so much black and white thinking.
Oh the irony! All you have done is disapprove of their mother. And your black and white thinking remains, examples of which are in this post. You will not have the children. Bottom line.