yes, this has been my experience, the second child makes a huge difference (and the first child's needs change as s/he gets older).
That book "3 socks and no hairbrush" (or something similar) makes the point that the first child takes up the slack in your life and when the second arrives there is just no 'space' for their needs to fit into. Also to my mind the extra aspect of life which is their sibling relationship adds yet more to the task, when you have to deal with jealousy, arguments, and so on, and just the simple fact that the two children don't need the same thing at the same time. For example a 4 year old can get her own coat on but needs her bottom wiping. A baby will stay where she is put but cannot go and fetch her own shoes. So you always end up doing double the work at every stage of the day.
When you have one child and 2 parents living together it doesn't seem too tricky to balance work and home. But the second child tips the balance, to the point where I think you absolutely need to have 'home cover' available every day when they are still young. How that is achieved depends on your circumstances. I guess the majority of 2-parent families solve it by one parent becoming a SAHP. Our own solution is for me to work 4 days and we have a live-in nanny. I am not at all sure that this is the best solution for us, but it is OK. Other families manage it by both parents working part-time or flexi-time. Even if you have a nursery or childminder, there are 2 x as many days for one or other to be sick, or just miserable and needy, 2 x as many doctor and dentists appointments. I also found that the "post-natal craziness" (excellent phrase) was more intense than I had expected, and still to this day 2.3 years after my second child I have not managed to 'take stock', although I have gone back to work and taken on a new role, all without really having a clear decision about it all.
The only suggestion i can offer is to try to think about what your own personal growth was going to be pre-children. I mean, were you thinking in terms of promotion, career change, sabbatical to study or travel the world? next, think about whether your feelings about that changed following your first child. Did you have to cut back hours, is that when you went part-time, and how did you feel about that at the time? I am assuming that as you mention school drops, your elder child is 5+ and things had settled down a bit. If you had not had second child, how would your work life have developed?
next, is there anything you can do or must do to keep a foothold in any of that? If you do step away from work for a substantial period of time, what would make it easier if/when you wanted to return?
is your Dh any good at talking these sorts of things through with you? it can be hard to express these thoughts without putting your partner on the defensive, I find. Whever I have tried to think aloud around these issues, DH gets cross with me and starts demanding what i want him to do.
not sure how much help this is, I think my rambling response just shows how I have not oragnised my own life let alone being able to formulate a response to anyone else's.