I imagine between yours and dh's work, trying to homeschool and keep house plus look after a toddler, your home life is quite chaotic right now.
Slow down! It's ok not to be able to do everything.
Your youngest is finding herself in the midst of a pandemic so hasn't had the normal route of socialising and parenting groups/meeting up with friends that many parents would have done.
Do you work from home or outside? If you and Dh are both working from home is there anyway of shifting some of either of yours working hours so one of you can do some in the evening while the other focuses on bedtime routine?
I would go back to the preschool and ask if they can have her even for one day a week, just to help you out until she can take up her place fully.
Create a routine which, for now, is set in stone. If you haven't achieved something within the given timeframe, move on to the next thing. It will help your little ones know what is coming next.
Parenting children who do not sleep is one of the hardest tasks ever I think, because it impacts on our sleep and then our performance during the day. Bedtime routines are a must. It was a sanity saver in our house. 'Return to bed' is a less controversial method of cry it out I think. As others have said, no light, minimal speech the first couple of times. Silence but gentle return to bed after that. We used to tuck a worn t shirt in with our youngest when they refused to sleep. The close comfort of something their parents had worn did help. Maybe sleep with one of their cuddly toys yourself for a few nights.
We also used to do bedtime story when they were tucked up in bed and put either an audio book or soothing music/sounds on a CD player. Alexa has a marvellous soothing sounds repertoire and even now our 8 year old is out like a light when we put jungle sounds on.
But most of all, be kind to yourself. As I said before, it's ok to not get everything done. Children need a lot of reassuring and right now I suspect a lot of them are picking up on their parents anxieties about stuff.