No one would expect you to leave a 2 year old alone. It must have been very frustrating trying to work through the changes. This is the kind of thing gate agents work hard to fix. They understand this is not acceptable. Glad the agent was able to get 2 seats together.
It's entirely possible my tip below wouldn't have helped, but it's good to know going forward.
I've learned to do a quick check on our booked flights about once a week. It allows me to catch changes usually before an email goes out. (And sometimes they never email...) Changes in equipment or schedule, I like to have first pick of getting things fixed. If it's equipment change, I may need to re-select seats together. The computer system doesn't always put us together or in the part of the plane we prefer.
If it's schedule, sometimes the change they have made is fine, sometimes it's not. If the timing is a problem-and I'm eligible for a change- I call and choose a better flight time. (I look up the options online ahead of time. Usually they will go with my choice as long as it fits within the rules.)
This doesn't solve every problem in the book, but it's helped me many, many times, and maybe it will help someone else.