Why does my potato bush not flower?
The phosphorus in the soil may have been depleted. This is what helps with flowering. Bone meal is a good organic ammendment to fix this. You can also use a high phosphorus fertilizer (typically sold as a 'bloom booster' fertilizer).
I want to remove a potato bush tree that is blocking an entry to the yard
I would recommend cutting it down, and digging out the roots. This article will help: https://www.gardeningknowhow.com/garden-how-to/projects/removing-existing-plants.htm
And will it come back in the spring?
No, these are only hardy in zones 9-11. Planting these outside will lead to a very quick death of the plant. It will need to be treated as a houseplant only.
This article will give you more information: https://www.gardeningknowhow.com/ornamental/shrubs/potato-bush/potato-bush-information.htm
I have 2 solanum as standard bushes in decent size pots at the front of my house which is mainly east facing. They have bloomed profusely and I’m very pleased with them. Approx 3’ tall. I’ve kept their ball shape, just by gently using secateurs. They’ve nearly come to the end of their flowering period and would really like to keep them over the winter to bloom again for next year. Could you tell me what I need to do with them. I have a small conservatory that I can use but no greenhouse
Your conservatory should be fine for overwintering your plants if the temperature stays above 40 degrees F, but does not get warm enough to confuse them. If your weather gets extremely cold, you may want to consider mulching around the base of the plants and even wrapping them with protective material.
Here are two articles that will help: