My PI is irresponsible and I worry about my career as a postdoc
Of all you say, the only indication I see of irresponsibility is his desire, you say, to send you back to the lab before it is safe. The rest is understandable. 

We live in perilous times. He may be entirely correct in focusing on his parental duties and may have no other option with child care essentially non existent in many places. Many people are depressed now, but it isn't a sign of lack of responsibility. "Forcing" you to write a grant can be a boost to your career and he might have wanted to do that in the best of times. 

Not getting accepted into the top journals can be pretty common and may not be his fault, or at least not entirely. 

And yet you say he has many good qualities. 

As to what you should do, I recommend that you maintain social distancing for your own safety. But beyond that, just carry on as best you can and hope that the horrors of the current situation don't increase or become cyclic. Make sure that you don't burn bridges with your professor, as that will make your next career steps (after the pandemic) much harder. 

Encourage the professor to deal effectively with depression if you can, and deal with your own if you feel those twinges. 

You are in a bad situation. A worldwide pandemic tends to cause that. It is no consolation, but in other times and places it was much worse. 



Another consideration you might make as to the level of his responsibility is how helpful he is at getting postdocs their next position. If he gives good support and they wind up in good positions, then you can put up with some things that wouldn't make sense otherwise.