Haha...I am a bit of an expert on Marco Island, so I'll recommend the JW Marriott on the island. I hear the condos are nice as well, but I've never stayed in either (just know the rooms from friends visiting).
You don't say how old your kids are or how long you are staying for, but Marco will certainly deliver on beach, weather, and easy meals for the kids. The Marriott does get pretty crowded in April (we are usually here for a month around then), but the beach is huge and there are always sections (particularly if you want to walk towards the norther for 15 minutes) where it is very quiet. I think they are almost finished the construction of the conference center (repeatedly delayed by hurricanes and some self-inflicted issues) so that shouldn't bother you too much.
Eating on Marco Island is generally fairly basic and most places that you'll see are geared towards the tourists (for example the forgettable plaza very close to the Marriott). There are a few 'better' places to eat. Sale e Pepe in the Ocean Resort is probably the most ambitious restaurant, though it can be hit and miss. Beautiful views of the beach from your table! CJ's on the Bay is fun as well, and then there is the Snook Inn at the back of the island. There are plenty more places, so feel free to PM me if you choose to come here.
You'll need a car. Even if you are only there for a week, you will want to get out and about. Naples is nice (great restaurants on 5th Ave and 3rd Street) and has good shopping (Waterside Shops). Miromar Outlets in Estero is a 40 minute drive north (useful in case it rains at the beach).
Greetings from a sunny Marco Island!