Unless you go to the Canary Islands or Maderia then no part of Europe is likely to have decent weather. In the Med it's likely to be cool and wet. If you want to go somewhere warm then look at the Red Sea coast of Egypt. Alternatively do what most people who take a holiday at that time of the year and go skiing in the Alps.

If you want warmth then the Canaries are the place to go. Plenty of islands to choose from, each very different from the next. The greener islands are the western ones. I personally love La Palma, small, green, good walking. You could rent a house there fairly cheaply for a week, preferably on the western side of the island. Car hire is also really cheap. The almonds should be blooming in February.
It is a popular time to go so if you decide on one of the islands book asap.

http://www.islalapalma.com/en/

http://www.thomson.co.uk/destinations/europe/spain/la-palma/holidays-la-palma.html for a cheap flight.

Try to avoid the big hotels and Los Cancajos though.

Have a look at the other islands too of course - one of the others may suit you and your family better.

Agreed - no where in Europe will give you warm weather in Feb. All my friends here head south to India or Africa for sun and warmth in Feb. My friend went to Goa this year, another went to Egypt last year and the Red Sea, or the Seychelles. Or the Canary Islands...

Half term is very popular travel time so book as soon as you can!

Or embrace the winter and head for northern Scandinavia or to Iceland - it is supposed to be a great winter for the the Northern Lights. Dog sledding, snowmobiling, snowshoeing and the chance of the lights.

Aahh deepest darkest February. I don't mind that grey, cold, last-of-the-mulled-wine time of year so I'm not always looking for "winter Sun", but if this Winter is anything like the last two you might want a bit of respite. The Canaries are a good suggestion, and note the need to book ahead that has been mentioned. Otherwise, if you don't want beach but sand is fine, then definitely look more at Morocco. It's interesting, has different parts to explore (cities, Atlas mountains, beaches/coastline) and would certainly give you warmth.

Or you could look at a week-10days in Sicily. Whilst it won't be warm enough for swimming (well, what I consider warm, but then my rule is no swimming in the Med until 1st June!), it is certainly sunny and warm enough for a T-shirt during the day and light jacket in the evenings.

Cyprus can be very pleasant at that time of year (15-20C during the day), with wild flowers in bloom (eg the almond trees in flower which are beautiful), snow in the higher peaks and lots to see minus the crowds. However it can rain and is cold in the evenings with frost occasionally, it still winter after all. English is widely spoken. There are some great hotels in Cyprus too.

A little further afield is Dubai, another popular winter destination. Otherwise, as others have said, Canary Islands, Egypt or a city that is beautiful in the snow eg St Petersburg, Stockholm and countless others.