infidelity, if proven in the court system, can give you the upperhand on the aspects of divorce.
the children deserve both parents, regardless of infidelity.
unless she is a unfit parent, in which i would think you would have mentioned, don't take the children completely away from her.
i am sorry that your family has to deal with this kind of problem. it seems so many of our children have to be in torn families these days. we as adults should be better and more mature about our daily decision making.
your mother will always take your side, becuase she is your mother. of course she wants you to move home with the grand kids. she wants to protect you and her grandchildren, and she also wants to punish your wife for her behaviour by alienating her from her children. that's perfectly natural human nature.
however, you need to choose the best solution for your family. if moving would be your best choice for a 'new start' go with it. just remember that you have two wounderful innocent children that are affected by your actions.
if you could, you should tell your wife that her actions have indirectly hurt her children. she may have not even thought about them while she was being selfish. she may actually start to realize that she needs to get herself together, and get back to being a mother instead of having an alternate life.
good luck