sus, on the work side, I think it is a case of how supportive your line management is, and how flexible you can be. I did tell my line management, but not in detail (though I was practically hyperventilating whenever I had to talk about it, so maybe it was obvious). I just said I thought they should know. My job is semi-flexible in so far as certain things I need to be in the office for, others I can do at home when dc are asleep. There are certain things, ie travel, I just can't do as a single parent, at the moment, maybe when they are older.
I did say when I told them that I would endeavour to keep doing my job to the best of my abilities, etc. As it happened I did need to juggle my work around at one point and take leave, and because it was odd days, rather than a block, I was upfront about why.
I think if you need time off, take it. I found that work gave me a sense of normality, because, quite frankly, no-one cared. They care about the job. I mean that in a good way, not that I work with a heartless bunch, but it remained professional; also I did say I wished to keep personal stuff private. Over the long term, as I had a heavy workload and the personal stuff was stressful, there has been an effect. I feel like I need time off.
In your case, I would be tempted to see if there was a way of changing your hours and working patterns around the school run. This will not be the situation forever, as you will in time sort your own living arrangements. But they may be able to accomodate your short term difficulties. Equally, keep your health and wellbeing needs in mind, if you need to take time off.