When we did our switcheroo (from Beach Club to Poly), we simply dropped our bags with Bell Services for the transfer, spent the day at the Magic Kingdom, and then headed straight to our resort after the 3pm parade (so we were arriving right at check-in time). Our bags had arrived long before and we just had to call Bell Services from our room to bring them to us. (We tried to stop at Poly Bell Services and pick them up, but they refused to give them to us (!??!) and insisted that we call from the room. Little did they know, the reason we tried to do it ourselves was that we realized we had no cash on hand to tip them...)
If you're headed to the Beach Club, I suggest you drop your bags for transfer in the morning and head to Epcot for the day (perhaps with a table service lunch reservation to give the family a mid-day rest). If you think there's no way the 2-year-old is going to last until check-in time, you can always check into the Beach Club right after lunch (even if your room isn't ready yet), so you'll all have access to the amenities, and grab some lounge chairs by the pool (or if you're staying in a DVC accommodation, the DVC building has a quiet little lounge called the "Drawing Room" on the ground floor just off of the foyer, which has sofas and chairs, a TV and a pool table) until your room is ready. The Beach Club is an easy 5-10 minute walk from Epcot's World Showcase.