If the new role is in another department but still the same organisation or similar, could you negotiate the same flexibility, in terms of the four-day week, or condensed hours. With the added commute, are there options if the trains are late/delayed or there's strikes? Will the added time impact your childcare arrangements? And, most crucially, does your partner share the childcare pick ups, drop offs, and sick days? Do you have a support network for the days you're both up against it and there's poorly children, or no transport, or nursery is closed or....?
Do you know much about the new department? Are people usually 9-5, for example, or are they often working late or having to do extra? Are there options to work at home, or work flexibly, if needed? It sounds like you have this already, and it can be priceless. It would be good to know more about what the expectations are, just to know if they align with what you'll be able to give. When I worked in the public sector, no-one batted an eye if I headed off at a particular time to sort the school run, but when I moved to the private sector, it wasn't the norm and it quickly became clear that it was causing issues, despite what they promised.
I've always felt more ambitious straight after a period of maternity leave and have wanted to climb the ladder, but I'm also very mindful of the pressures that come with juggling a new job, new people, new expectations and a very young family, but with the right support, there shouldn't be any reason you can't smash it!