I have been divorced from my ex-wife now for three years plus, and from that marriage I am blessed with two boys ages 6 and 11. Both of my boys stay with me every weekend without fail, as I don't live far away from them. My eldest son (Kamran) has been asking for over 2 years now if he could come and live with me and my partner. The last six months however he has been quite literally begging me to let him stay. Obviously I would love him (or both) to live with me full-time but I am completely unsure how to go about this.
My ex and I separated on o.k terms. I left her with the house, which she pays the mortgage for. I also agreed at the time that the children would be better off staying with their mother as I didn't think a custody battle would be helpful to the situation.
Now, however, I'm concerned that he isn't happy with his mother. His mum was never very maternal when I was with her, and from what I can gather still isn't. By subtly enquiring, I have found that she doesn't assist in their schooling what-so-ever. This was the case when we were together, and to be honest I enjoy listening to them read, assisting in spellings or other projects they both have.
Other than that she has no interest in playing with them at home or going on days out, or even watching them play a football match. I'm the complete opposite of this and so is my partner of 18 months.
I know that their mother loves them both very much, but unfortunately I think her up-bringing has lead her to be very selfish and will only involve herself if she benefits from the experience, I.e garden parties where alcohol can be consumed.
All I need to know is where I stand about this. My younger son also says he would like to live with me but I feel this is more to do with repeating what his brother thinks, rather than anything else. Khalam's a happy child and doing well at school so I'm not as concerned with him as I am with Kamran.
Please any advice will be helpful and appreciated.

You have to file for a modification of the custody order in court. At 11 they may listen to you son's preference but I doubt if they will give it much weight. You will need to convince the court it is in your son's best interests.

I would strongly suggest getting an attorney to help you prepare such a case.

Have you asked the mother if she will agree to allow him to stay ? If she says yes, have the attorney fill out a motion to modify the custody and child support agreement and both sign and file at court.

If she will not agree, it gets dirty and you have to take her to court and show the boy ( or boys) would be better off with you, file for custody and child support and have child testify to what he would prefer, if old enough for court

...I think her up-bringing has lead her to be very selfish and will only involve herself if she benefits from the experience, I.e garden parties where alcohol can be consumed.
...

If you are suggesting such garden parties are not in your childrens' best interest, you will want to be clearer, if you bring this up in court so as to attempt to make some sort of a point. Alcohol consumption as such, and not to excess, is not necessarily a bad thing, even in the presence of children. It may be a cultural taboo for you, but don't assume everyone shares your viewpoint.