What was your set up before you were on furlough and DH was WFH?
I would sit down and write down what things looked like before and what they look like now.
DH shouldn't be the sole beneficiary of no commute. If timings begin at whatever time DD wakes up (say 7am but suspect that's wishful thinking) I would suggest the following:
7am - 8.20am, everyone needs to eat and shower/get dressed for the day. Equal split of time to get ready themselves and be responsible for DD getting ready for the day and being occupied
8.20am - 8.30am, DH upstairs preparing to start his working day
8.30am - lunchtime, DH working and pretend he isn't in the house, DD sole responsibility of lilac
Lunch hour - lunch is prepared, everyone eats and DD responsibility of both parents, maybe family walk or 15 minute break each
After lunch hour - 4.30pm, DH working and pretend he isn't in the house, DD sole responsibility of lilac
4.30pm - 4.45pm DH wind down from work mode upstairs
4.45pm - DD's bedtime, Dinner for all prepared and eaten, occupy DD, DD bath time and bedtime. All tasks joint responsibility of both parents. Both parents don't have to be 'on duty' at all times but time is equal
Post DD's bedtime - both spend evening together/apart as agreed once all household tasks are completed jointly
This is during work periods while you are on furlough. Weekends all tasks, responsibility for DD and alone time are split equally.
I suspect the current 2/3 trips to the toilet by DH are him hiding with his phone. Suggest no phones in the toilet or trip to the doctors to sort out what must be quite a serious medical condition.
WFH is a nightmare for lots of people. I wouldn't want to have to try and keep children quiet in their own home to enable one parent to work. It's a bit like trying to keep kids on their best behaviour while out. They do need a safe space to vent and to suddenly have that taken away is really difficult for everyone.