There is a dedicated thread on this forum about transfers in WAW - a general consensus is that WAW is one of the most efficient/easy EU airports for transit. There are some kid playground areas on the departure level, but not in the lounge.
Two years ago there was an area in the Warsaw lounge (Schengen) for travelers with small children. The entrance was hidden a bit (somewhere behind the first food serving area, if my memory serves me right) and the door was sometimes locked and I had to ask at the front desk that the room is opened. Used it several times and it was brilliant (toys, separate toilet with a changing table, etc.). Haven't used it in a couple of years. Perhaps someone who is a frequent visitor there could verify its existence.
I flew with my son when he was 15 months BRU-IAD in C on UA (day time flight). Frankly, it was a horror trip. He had just learned how to walk, so he was practicing. Some people fly over the Atlantic, I walked over the Atlantic with him back and forth in the aisle. I must have driven everybody crazy. It was either walking or crying. He was not interested in anything else. The overnight return was a piece of cake - he slept.