Be happy that you found out about this ahead of time. It's much better than showing up and not having a bathtub and not having a back-up plan. Now you have options:
1. Request a room with a bathtub. If you don't get one, go to the front desk and request it again, they might be able to move you to a room with a bathtub.
2. Take a toddler-size inflatable bathtub with you so you don't have to worry about it. Or, take a flat rubber jar opener to put over the shower drain. Assuming there's somewhat of a ledge on the shower, you can get a few inches of water for a make-shift shallow bathtub. I used to have to do that when I had a toddler and lived in a house that only a had a walk-in shower.
3. Change your reservation to a different resort. The All-Star resorts are currently undergoing the same type of renovations that Pop Century has so chances are that they will have the same issue. The Little Mermaid rooms at AoA will be the last ones to be renovated so if you're going in the next year or two, those rooms should be "safe" and guaranteed a bathtub unless you get a HA room.
I can understand how this could be frustrating for you. We traveled with young kids for many years (we have 5...seemed like we *always* had a "little" one). If they were young and didn't like to take a shower and we ended up in a room with no tub (I'm talking about non-Disney places), I would either do the flat jar opener trick, or I'd just wash them by the sink. Fortunately, our kids were fine with showers by the time they were about 2. They didn't necessarily want to stand under the shower, but they were willing to stand in the shower stall while I washed them with the flowing water.
I personally am one of those people who is happy that Disney is putting walk-in showers in some of their value rooms. While a lot of families with young kids *do* travel to Disney I think there are even more with older kids or no kids who are traveling to Disney. I would estimate that less than 25% of guests have kids under 2 or 3 (when most kids are willing to try a shower). My husband has an artificial hip and it can be challenging to step over the side of the tub after a long day in the parks. We're very happy to have a walk in shower in our suite at AoA. Our challenge when we no longer stay at AoA will be the opposite of yours...we'll want a room with no tub and only a walk-in shower. I think Disney is trying to accommodate a variety of guests as it's not just families with young kids who spend their money there.