My Father wants a green card to live in US. He & American Mom live in UK - I live in US. Better to apply in UK or here in US??

Based on your question, I am assuming that your mom is a USC. If that is the case, then she could file the petition for your dad's green card in the UK through direct consular processing b/c she currently resides in UK or you could petition for your dad (assuming you are at least 21 years old) here in the US. Some say that consular processing is faster than regular processing of I-130 here in the US. There are other things to consider, however, so you should consult with an immigration attorney experienced in this field to assist you. Because immigration is federal law, an immigration attorney in any jurisdiction may assist you.

They spend their winters with me here in US, but Dad can only stay four months on a visitor visa. Would that be enough time to apply and get legal residency with a Green Card? It would get expensive if he had to leave and go back to the UK if his visitor visa would run out in the middle of the application. My mom would probably apply for him as they have more funds (re sponsoring critieria) than I do, but she is elderly and I would like to be physically with them to help with their paperwork and appointments etc.

If you would like to help your parents with the application, then you can file the I-130 for him here in the US. Once it's approved, the AOS can be done in the UK. He does not need to be physically present in the US during this time, so you don't have to worry about the 4 months. If your income is not enough on its own to sponsor your dad, then you can find a co-sponsor - i.e. your mom, your mom & dad's joint assets, etc.

As I mentioned before, before you submit the I-130 application for your dad, please consult with an experienced immigration attorney to help you discuss the details of your case/situation. Only then can you decide the best strategy. The answers here on this board are only meant to be informational.