Like you I work full time while DH is at home with 19 month old and 4 yr old. Many a time I have been pissed off at the state of the house when I have walked in - just general mess, no vandalism but that's just because my ds hates drawing otherwise I'm sure I would have had that too.
However, ultimately I know that my dh does a fab job. He is involved with the dc all day, he focuses on them. He doesn't do everything my way and, like you, I feel he is more laid back than me, unlike you I see that as a good thing as I am a bit of a controller.
You can't make your dh do things your way, as long as he is concentrating on them all day and they are not just in front of the tv while he amuses himself then the other stuff really doesn't matter. Regarding the front door incident, surely we have all had stuff like that happen where a child surprises us by doing something potentially dangerous they've shown no sign of doing before. I know I have. As long as steps are taken to ensure it doesn't happen again then I think you need to let that one go.
My dh does go to a toddler group occasionally but he more often goes to the park and has made a few friends there - he found it less intimidating. One of the highlights of the week is changing the bedding in our room, they turn it into a huge game apparantly and it takes most of a morning. I've been off this week and saw for myself ds1's face light up when dh mentioned changing the beds! It wouldn't occur to me and I'm not keen on the ensuing mess but they are happy so, ultimately, so am I.
Tbh, I think that part of your problem is that you used to be the sahp and that has changed (aplogies if this is not the case) It must be hard to adjust and see your dh not doing things your way but I think you need to let him find his own style. If you come across as angrily to him as you seem on here then he is likely to get defensive and feel he can never please you.
I think you need to set a few 'rules' and then let him get on with it his way. Ours are that dh tidies up while I put the dc to bed and I have convinced him that letting ds2 play with the boxes of jigsaws etc is silly as then we have nowhere to put stuff. That is it. He is in charge in the day, I'm not even here so he has to do stuff that he feels comfortable with.
The bottom line is you have to trust him and if you really don't then you shouldn't really be leaving the dc with him anyway.