Hi Mayla, she clearly means a lot to you, and to me it sounds really good that you've found each other
And other than a few practicalities which there might be ways around, do you think that the depression as much as anything is telling you that you're "letting her down". And you know how depression can leave you feeling that you're not doing enough, you're not good enough, you're failing at so much, you just can't.............., you're more of a burden, right?? But that doesn't mean any of it's true does it?!
Maybe when she's not doing as much, lying around a bit..........it's a sign that she's feeling settled and content, which is good, right?? And there's nothing to say that she isn't picking up on the love you feel for her as well.
Now you have got a great base to work from with "I do the essentials--feeding her twice daily, taking her out when nature calls, giving her some play time both outdoors and indoors". The commands..........maybe you'll get there, maybe a short time each evening to give it a go.......maybe there's a training school somewhere in your area someone could take her to..............but otherwise it doesn't really matter that much does it?? If she's contented and pretty well behaved (mostly!!) that's alright isn't it??
And the walks.........well perhaps you could find someone to help with them?? I don't know your area but.........maybe a neighbor, putting an ad in a newsagents, school, college, local vets?? Needn't cost that much. Or some rescue centers have volunteers, maybe you could ask them to turn someone your way if you explain the situation?? And you could still give her some walks yourself as well, yes??
And where you can become just a little more engaged..........maybe start by scheduling in an extra 5 minutes in the evenings, although like I've said she might be content anyway.
And you're working on the cleaning anyway aren't you?? Maybe just have a think about what jobs are a priority, focus on them.........and the rest........just work on trying to fit them in when you can, they can wait a bit longer, right?? Try not to be too tough on yourself
Then just the family , maybe try to foresee some of the risks around and get some systems in place with them to/ask for them to agree on some guidelines???
Don't make any snap decisions about not keeping her though, it sounds like she's very important to you and that you love her a lot. Hope you can work something out.

Alison