Hi marion, what you describe is not possible - cross pollination only affects the seeds and cannot change the variety of an existing tree. What can happen is that branches can grow from below the graft point (virtually all apple trees have the named variety grafted onto a different rootstock.) If branches are allowed to grow from below the graft, they will produce apples of the rootstock variety. As rootstocks are chosen for their vigour and not fruit, these branches will usually take over and become dominant. Have a look to see if you can find the original graft union and remove any branches which come from below that point.
Mildew can also badly affect a tree enough to change the quality of the fruit. It is difficult to deal with but generally is due to dryness at the roots and high humidity in the air. You can do little about the humidity, but giving the trees a regular and deep watering should help with the dryness. My advice would be to keep a circle of ground, about a metre in diameter around the base of the trunks, clear of grass, weeds and other plants. After watering them well, mulch this area with a good layer of garden compost mixed with well rotted farmyard manure from a garden centre. Top the layer up each Spring. Also make sure you are pruning the trees properly so that their is plenty of light and air getting into the centre and ensure the trees are not being overly shaded by surrounding trees and large shrubs.