Question
We have a peach tree that is bearing fruit.  We have had it for 2 years and haven't pruned it before.  There is a long stem that has taken over much of the tree coming from the trunk.  A couple of months ago I did cut this off because I thought it was a weed.  It was bright green and the rest of the tree was a purple color.  Now this same stem is taller than tree.  The peaches are small and hard which are on original trunk.  How do we prune and what can we do get nice size peaches?

Answer
That green stem is called a "sucker". All suckers should be cut off at the base of the stem where it grows from the trunk. They will continue to come back, so you will need to keep them cut off. They will never produce fruit, and sap strength from the tree.
The difference between the "dwarf peach", and the "patio" peach is in the breeding. Both trees are graphed trees. That means that the dwarf part of the tree has been attached to a standard tree. The result for the dwarf tree is a dwarf Elberta, or Cling, or other good eating peaches. It is too large for container growing, and does well in good soil in the garden.
The Patio peach is not intended to be a good eating peach. It was bred for a small, attractive, container tree. The fruit is not very good. ( The sucker is growing from the standard tree, not the graphed part.)
Your tree is still young. As the tree matures, and it is potted up to a large container, it will produce more large fruit. They are slow to ripen. But when they do, I recogmmend mixing them in a pie or cobbler with a sweet fruit, like strawberries, or cherries. Cooking will soften, and sweeten them, making them better to eat.

Prune in early spring. When new growth starts, cut to shape the tree in a round lollypop shape. Stand back and look for limbs that make the tree unattractive. The more even the shape, the more pleasing to look at. Cut just above the leaf. The new growth will start there.