First trips to Walt Disney World are the most magical of milestones, Adrian. I'm so excited for your family! To answer your question I took a look at free dining promotions that have been offered in the past and I'm pleased to report that free dining has been offered during the week you want to visit for the last several years. There is no telling whether the same will hold true for this year or not, but if it were me, I'd keep my eye on the Disney Parks Blog and the
special offers page on the website. If an announcement is to come, I would expect it to happen in July or August, based on historical announcements of that promotion.
My ideal length of stay is significantly longer than four nights; I think a ten day vacation is perfect, though I know a lot of people who visit for shorter stays and fit a whole lot of magic into a short time! Since you are looking at a relatively quick trip, I would advise you to stay in a monorail resort if you can swing it. With children as young as yours, you'll likely be spending a majority of time at Magic Kingdom and the monorail resorts are the most convenient to that park. Staying in one of those will help maximize your touring time.
If I can be of further assistance, please don't hesitate to ask me follow-up questions. Have a great time!