airlines don't always book legal connections. I've had them give me connections as short as 15 minutes and even once the connecting flight left before the other flight landed. The agent had a great laugh about that one.Based on my recent experience (I've done probably 90% of the flying in my life in the last 4 years), I disagree. Actually, I saw it happen the last time I flew, which was last week.
Regardless, if the airline booked the OP on a new connecting flight, they had to book her using legal connection times, so depending on the airport, she likely has at least 30 minutes, and probably closer to an hour, to make the connection. That doesn't seem like a long time to make a flight when you're traveling with a toddler, but this is likely a moot argument.
Given the fees and fines that are now associated with planes pushing back late, I would not rely on the airline holding your flight.