Travel between UK and ITaly in Schengen area

As US citizen I am able to be here in UK for 180 days out of 360 days from my date of arrival. On Dec 7 I leave UK after being here for 176 days  I am traveling to Italy and Portugal -in Schengen area where I can be 3 months within a 6 month period.   

I need some clarification on how to best travel between Schengen area countries and UK or non-Schengen area over a 2 year period.
Can I be in Italy for one month, and then travel to Portugal for two months, then return to UK for three months, beginning a new 6 month stay in one year, and then return to  Italy for three months, and return to UK for three months?
When does the Schengen area (90 days within 180 days) start in the Italy?  Portugal?

I have heard that it is possible to be in a Schengen country for 3 months, stay in a non-Schengen area country for a few days and then, when I return to Schengen area it begins a new 6 month period.   Is this possible?

Any advice anyone can share with me on this will be extremely helpful.

Hi,

I heard the same too.. I am currently in Italy, as a Malaysian I have 3 months stay period under tourist visa, as we are processing my documents for long term stay ( spouse visa) we are trying to squeeze everything that need to be done in 3 months, but if not then I need to make a "U turn' from Italy (Schengen country) to UK (a non Schengen country) stay for 4-7 days then back to Italy to get another 3 months visa.

This 'U Turn' is possible according to information we Googled and friends that work in Immigration offices. So if it possivle for me to do Schengen to non-Schengen country, it must possible to you to do the other way around.

Cheers.

Yes Sarah I have already done UK -Belgium-UK.  Thanks for your info.   Hearing that the 3 month period was per country(!) was contrary to total of  three months in Schengen area.  I understand some countries are more strict than others, but to me it is not worth the risk.  All the best to you