Wow. I thought the op was asking what to do WHEN taking the kids to Europe. Obviously, English is not my first language.
Just in case the op is still around - I'll add some resorts I would consider myself. Please do keep in mind that I do not think Europe has many great timeshares and I think hotels are a better option in many places.
Interval:
All Marriott resorts. Although I am not a huge fan of the Spanish locations, I love the resorts and I don't think you can go wrong with any of them. Beaches at the Costa del Sol are not great as mentioned before by another poster. I think the French resort is a great spot to explore a part of Northern France. There is so much to do in the area - apart from Paris and Disney.
The Royal Savoy (Madeira), Golden Sands (Malta). The De Vere resorts in the UK.
RCI:
San Lawrenz resort (Gozo) which is part of the Kempinski San Lawrenz hotel. There are only 9 timeshare units so this may be very hard to get.
Some of the Pestana resorts in Portugal/Madeira. There is a resort which is part of the Le Meridien in Cyprus, but I forgot the name. Some resorts in Greece, like the Classical resort at the Marine Palace Suites.
If you would consider hotels:
Keep in mind that Hilton offers a 2nd room for children for 50% of their best available rate, or any flexible rate. They offer this at many European and Asian hotels. You might have to call HH or the hotel.
Accor (Novotel) is pretty good when it comes to connecting rooms and rooms which sleep up to 4. So is Holiday Inn.
Hilton is good with connecting rooms as is Starwood, but they will mostly accomodate 3 per room - which may be still good for your family.
Marriott is not very good with connecting rooms; they are there, but not at all hotels.
Some hotels my kids like:
Hilton Sorrento - not luxurious but very kid friendly. Italians love bambino in general, and it does show at this hotel.
WA Rome Cavalieri - but you may want to have HH diamond status in order to use the pool loungers without any additional fee. Especially when taking kids to Rome during summer - they will be very happy having that pool.
Starwood and Marriott have hotels in Italy too of course, but my kids love the 2 Hiltons.
Hilton Malta, Westin Malta.
The Romanos and Westin Costa Navarino (Greece) - location is wonderful especially if you want a more "authentic" taste of Greece. Blue Palace (Starwood, Greece)
There are so many more options; I am sure I missed a few great ones.
Turkey has some great options for children. When my kids came to the Atlantis for the first time, they were disappointed with the pool features at first because their expectations were set too high. Turkey has many hotels with terrific waterpark-like features. Turkish people love kids and their hospitality is very hard to match. Hilton has 2 new resorts, but I don't think they have these waterpark features. Marriott has the Renaissance Antalya Beach resort which is great but older.
Just a general tip for traveling with your 2 yrs old: make sure you have a stroller which folds in/out easily (think taking cabs and such), and which has a recline feature. Just bring some favorite snacks and keep them for "special occasions".
For all kids: Keep a small bag for each kid with a few of their favorite ... (fill in the blanks). Hand it to them only if they are getting bored and you need them to be quiet for a little while. Let the kids return the goodies to you every time, so you keep control over when where and for how long. The contents don't have to be large or expensive and they don't have to be new. In fact, sometimes a few small things from home will do.
And please do keep in mind that not all kids are happy when traveling to various places during 1 vacation. My kids never had a problem, and they had visited all continents by the time they were 2. But our friends went on a 3 week tour through California, Nevada and Arizona this last summer. Their youngest, 11 at the time, had a hard time adjusting to the various hotels they visited. She ended up hating that vacation and she now refuses to go back to the US anytime soon. This wasn't her first time visiting the US, and she had been to Asia and Africa before. It just happened, and I think it had a lot to do with their itinerary.
Just to show that your 2 yrs old may not be your biggest concern at all. :ignore: