Completely unreasonable. Almost laughable, truth be told.
These costs unfortunately... well, it's life! You find a way. Simple as that.
I was 23 when I had my first. When I returned to work full time it was the worst off (financially) I could be. Best scenario was to quit my job and claim unemployment benefits, 2nd best was to go part time and claim tax credits to top up as best as possible, and worst was working full time (would have cost more to work, commute, and pay nursery than I earned!).
I decided part-time for the sake of my career. It meant that after 4 short years, when child was in school, I could go back to full time.
Sorry, but to expect your mother to do your job for you is extremely poor. Regardless of what other people's parents do. It's her choice and she is 1000% entitled to say do one.
I sympathise in that things are shit for new parents but it's always been the way. If its any consolation, it made having my second MUCH easier as I fully understood the impact of what being a mum meant to our income and finances.
Good luck,and buy your mum some flowers or bake her a cake to apologise.