We had a situation very much like your own with a child my son met when he joined scouting.
The mother was very similar, taking advantage of my family for the 5 years that we had contact with them, except that she readily would invite my son over for sleep overs so he could "entertain" (read babysit) her son. frequentcey of the visits increased as time went by to the point of being every weekend.
As the boys both approached the age of 13 the gaps in their mental maturity continued to grow to the point that I stepped in and pointed out these gaps to the mother, and explained that my son had other friends that he liked to hangout with too, and wanted to do typical teenage things that her son didn't have the mental and physical ability to keep up with, and that if she looked at it objectively she could see it for herself. This was not a poke at her son, or anybody learning disabled, just nature taking its course as the boys matured.
Of course the mother went into a rage and cursed me out, I expected that.
I calmly told her to think things over and maybe give me a call to tell me what conclusions she came up with, even if she just wanted to curse at me some more.
Next weekend she did call me.
She said she thought things through and she found she had noticed the gap between the boys growing and had tried to push those thoughts away.
She called months later to tell me of some of the programs she had gotten her son into as a result of my son breaking free from them, and that her son was really happy to be socializing with other children like himself, and much happier than he had been in the past, but once in awhile he would ask her how my son was doing.
I asked my son if he wanted to know how his old friend was doing, he said he'd like to talk to him, so I told him to call him.
They now call each other on birthdays and holidays even though its been 5 years since they've been face to face. ( the other childs family moved 4 states away)