We're fortunate to have somewhat older children, who need only short attention bursts followed by longer periods of working independently. However, with a 14 month old, you're not going to get that!
What several couples that I work with have done is split the time of the day up between them. For example, one couple who both work at my office and have a child of a similar age to your youngest do:
- 7am-11am: Husband works, wife watches kids
- 11am-3pm: Wife works, Husband watches kids
- 3pm-5pm: Husband works, Wife watches kids
- 5pm-7pm: Wife works, Husband watches kids
Both are able to get in six hours of work; that's not ideal, of course, but it's possible to do. If they need more time, they can work into the later evening once the children are asleep (fortunately yours are both old enough to sleep through the night, I hope!).
As far as housework, it's certainly hard to manage that I think in this sort of scenario. Our family (with two working parents who both mostly work during the day) is focusing the weekend on that; while we do the dishes during the week, and run loads of laundry during the week (our eldest mostly does that, fortunately), most of the rest of the housework goes by the wayside until the weekend. Then one weekend day is spent focusing solely on the children's fun - interactive games, playing in the back yard, whatever; and the other weekend day is a working day where we do the laundry folding, pick up, clean, dust, whatever.
That works well at the ages we have - mid-elementary ages - where the kids can at least participate some in housework, and can play independently for the most part. At a younger age, we likely would have simply coordinated the weekend as we do a work day - one parent focusing on children while the other works on housework. That's largely what we did when our kids were your age even in normal times.
That has the advantage that you can distribute housework to the parent more happy to do that particular type - my wife is happier picking up and cleaning, I'm better on the bills, scheduling schoolwork, and cooking dinners, we're both happy to do dishes and fold laundry; so we split it up and did those things we preferred during our 'work' times, and then did the things we enjoyed with the kids during our 'play' times - and occasionally had both-play times, of course, though probably less than we'd have liked - but such is the life of a two working parent household.
As far as showering and wearing clean clothes: I think these are very important, at least to the most part, because they're elements of normalcy that can keep you sane. I have video calls at work fairly often, and I am religious about turning the video on and making sure I'm in work clothes - not because I think it makes a big difference, but because it makes me make the effort to dress appropriately. Getting in the mindset of doing work is very important.
This isn't any different as a parent: comport yourself as you would have without this situation, as best as you can. Your kids recognize the difference between shabby, smelly mom and dad, and showered and dressed mom and dad. They might not care too much of course - but it does make a difference for the mindset you get in, and they get in, of "lazing around" versus getting things done.
That said, there's nothing wrong with having a day where you don't shower or get dressed and just laze around. That's true now just as it was before. Just don't make it often - and do it on purpose, because you think it's fun! Point out to the kids that you're doing it, have them wear their most fun pajamas all day (my eldest has the cutest dragon pajamas that are hilarious to wear, especially as a middle grade child), relax the rules.
But then, the next day, shower, dress in your more formal workday attire, and get back to work. Show the kids that you can do that, too, and that things are more like normal again.