My family is from Arco de Calheta, Maderia Island and I would like to take my grandchildren to learn about their heritage. Although I have relatives there I do not know there sir names. My family names are Teixeira and Souza. We are thinking of renting an apartment or villa for a month and make day trips around the island. We are looking at possibly going in May because the flowers are supposedly spectacular at time of year. Is there a better time of year to visit the island?

Well I was a single traveller to Madeira for 6 days in 2009 so I have no tips for you re family accommodation. But for your other questions: Teixeira is a famous family name in Madeira, IIRC he was Zarco's second in command, and I wouldn't be surprised if Souza is also famous. You're probably related to them.
The temperatures are pleasant pretty much all year round, you only have to watch out for the rainy days. I was there in October. They had severe floods in December that year. Here's an annual chart:
http://www.madeira-web.com/PagesUK/weather2-uk.html
Madeira is a volcanic island and the coastline is highly indented. If you have a car that's no problem but travel can take longer than it looks. With a month, you should have no problem. Do some hikes in the interior, the views are fantastic.

Try June or July for flower shows - these are displays laid out in the streets for the various zone celebrations (every village has its own annual celebration).
The weather is very good this time of year, if not too hot (30 degrees). As for accommodation, I have an apartment that is rented out - contact me by email if you are interested
mamameeya - Hello again......you wrote before the following in Sept 2010:
"Try June or July for flower shows - these are displays laid out in the streets for the various zone celebrations (every village has its own annual celebration).
The weather is very good this time of year, if not too hot (30 degrees). As for accommodation, I have an apartment that is rented out - contact me by email if you are interested."
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Obrigado for that information.....Please tell us more about your apartment. It would be for my wife and I. We are in our 60's. We are no "party animals." We will respect your property. We are thinking 2 -3 months. We will invite immediate family to visit for periodic visits - whoever has the time and money to travel - so, two bedrooms would be good, three preferred. For more on me, please see http://www.linkedin.com/in/davidgarrott. Look forward to your response.
Regards,
David