I don'y have DC, but was in a kind of similar situation once in that I felt I was doing and was under-performing and that I was being sidelined by my employer. Eventually, I arranged an appointment to talk to my boss about it. Turns out I was under-performing, but he had been so worried that this was because I was planning to leave that he'd been too scared to say anything! So the lack of communication had made things worse for everyone.
So we had a frank chat about how to fix things: I was under-performing because I hadn't been given any training or even a proper job description. So once we had sorted that out, and given me a set of objectives to achieve, things got much better.
So if I were in your shoes, I would have a chat to your line manager--not to pour out your woes, but to have a constructive conversation about how things are going and how to move forward. Emphasise your committment to the organisation and to doing an excellent job, but explain that you are worried that your day working from home, plus the fact that you need to leave at your contracted time are giving the opposite impression.
You therefore want to draw up a set of measureable SMART objectives for you to achieve in the next quarter so that your boss can rate your contribution to the company by your performance, rather than by presenteeism in the office. Make sure these are objectives that you can not only meet, but in some cases, also exceed (don't tell your boss that bit :) ) to demonstrate how bloody brilliant you are.
Your organisation has already allowed you to work form home one day a week: this, to me, is a string sign that they really value you and want to keep you. Keeping some good communication going between you and your boss, together with achieving the objectives you have set will really help you feel in contraol of the situation again and help banish negative thoughts.