Does this sound like an odd topic? You should see my current position in life. I'm a cat warmer apparently so I've only got my hands partially free to type. Now, there are several ways you can be trapped physically. You could be bound to the house due to a baby or young child, you could be like me and at the whims of various pets or there could be something else stopping you from getting up and moving about as you'd like. Whatever it is, usually it saps time as well as space from you. And as much as you might want to live like a hermit writer you probably can't.
This means that working becomes something you need to do around the movements of others or your other problems. Its a game of negotiation with oneself, essentially. You sort out what's most important to you first and then delve into your work. What's most important should always be such things as family, animal care and even the little things like feeding yourself and making sure the washing's done.
Most of the time though, when you're writing, it is the story that seems most important. Not to mention the deadline, whether self-induced or otherwise. You're understanding of what is the most important thing becomes confused when you're in the midst of things, meaning that what traps you and what interrupts you becomes a thing to fight bitterly. This can lead to you neglecting those around you, destroying the friendly relationship you have with your pets, letting the house sink into disrepair, possibly attacking people for being so irritating and even attacking yourself for not being able to control everything like you think you should.
If there's a baby in the house you probably also feel like your mind's turned to moosh so that even if you have some spare minutes here and there to write you couldn't think of a thing to write about if your life depended on it. Sleep deprivation and other concerns do that. But such times don't last forever. Also, laptops come in handy here so that no matter where you have that lucid moment the laptop is ready so you can write. And don't forget the pen and paper in the pocket so you can jot down any idea you have while on the hop (though sometimes actually getting pen to paper is difficult).
As I mentioned before, working while trapped is a game of negotiation. You have to give up parts of yourself in order to get other things done and you have to sacrifice one project for another according to how you're trapped at any particular moment. Things often don't go your way and the day's plan has to change but consider it this way. You're going to get it all done eventually anyway so the main problem you'll have is meeting a deadline for one particular project that is hard to do due to repeating circumstances.
In such cases you could negotiate with the ones setting the deadline or put your foot down with regards to any outside influences that are trapping you. Cats and dogs get thrown out into the yard, baby's sent to a baby sitter for a day's minding so you can really crunch through your work and older kids can go for a sleepover or something else fun (in return you might hold your own later so the other kid's parents get some time off too). If you're in the wrong house or minding someone who's terribly sick then a laptop and working during the other person's sleep or entertainment times is acceptable (particularly if they aren't really noticing what you're up to).
In cases of caring sometimes the other person just wants company and not talk, wants a distraction of their own so would like to help you or is relatively unaware of everything so having a hand to hold is the most they'd like. If you're in such a position as caring while meeting a deadline you just gage the other person's situation and needs and meet them. It may mean sacrificing a hand so you're typing one handed or taking half a day as a caring shift so that you can work the other half a day in a solid slog rather than be constantly interrupting your work for the other person or the other person's care for your work (however you see it at any particular point - yes, your view on it will always switch between the two so don't feel bad about that).
The aim is to negotiate some time and space for yourself to work solidly for as long as you possibly can before returning to the other important things in life. Saying that your writing is more important than anything else just because you're completely mentally stuck in the story is, and actively treating your writing as such, will only make you regret quite a few of your actions and missed chances in life. Overall, regret is something best not felt though it is rather unavoidable for most of us as we usually regret some of our actions. Still, even though we all regret something or another so should be fine with adding more, we generally aren't. So try not to make writing the be all and end all, to the detriment of the rest of your life. But at the same time, don't forget to write whenever you can.
I hope this makes sense. I've been scampered on, curled up on, clawed, had a tail in my face and a cat bum on my arm and laptop all while writing this. It is too cold outside apparently. At least they've settled somewhat now into a purring mass but still, I'm trapped flopped over sideways with one arm free only from the wrist and I don't think I can stay like this for long. It'll hurt.