Bit of background. We have two DCs aged 4 and 16 months. We've all been at home since lockdown began (we're in Wales so restrictions haven't been eased as much as in England), DH working full time and me part time. Monday's and Fridays are my days off. Neither DC has been back to any childcare setting yet, so it's been intense, but no where near as bad as I would've pictured if someone told me about this scenario a year ago 
DH didn't have the best example of parenting growing up, his dad is a bit of a waste of space and never showed much interest, wasn't very tolerant of children. His DM is quite traditional and adores our DCs but I think there was a fair bit of her bad mouthing FIL to the DCs, arguments and playing favourites with her own daughter. Nevertheless DH has happy memories of his childhood and we have a good relationship with MIL who has seen the DC a fair few times in lockdown for garden visits/walks.
DS age 4 is lovely. In lockdown he's been quite intense and needs an awful lot of input from us, is needy etc, but perfectly manageable compared with a lot of children I hear about. Bad behaviour is usually addressed effectively with either reward charts or consequences eg loss of tablet time.
DH is constantly on at DS, about small things which I think should just be ignored/not made a big deal out of. I'm impatient and won't tolerate things like throwing toys (toys get removed for a set time), nastiness to baby DC, so IMO I'm not letting too much go. Examples of the small things DH will pick at are:
- sitting at the table properly/spilling food. DS tends to sit cross legged or with his knees up, is clumsy and spills a bit of milk from his cereal on his pjs. He doesn't like wet clothes so sometimes will make a fuss. I ignore this, I might suggest he won't spill if he sits properly with his legs under the table, but I don't push it. DH will nag about the spilling, force DS to sit properly, DS ends up getting cross and shouting at DH, DH then gets cross...etc etc. Tiny things like this escalate a lot.
- messing round when he's meant to be getting dressed, deliberately putting things on backwards
- making "too much" noise when baby DS is napping. The noise is just normal kids' noise, baby isn't a great napper so I always try and keep noise to a minimum any way, but the things DH will pick at is eg closing the doors too loudly, dropping toys on the hard floor etc
- general irritating behaviour/pestering. Pulling on DH's clothes, getting his food covered hands on DH's clothes, touching food when we're trying to prepare it for lunch etc
This list is just an example, but the reason it bothers me so much is because it always escalates. DH always comes across as impatient/angry when addressing these types of issues. I can see that DS probably feels micromanaged, so he gets angry, which in turn makes DH more angry, it often ends up in DS in tears.
I suggested the book How to talk...as I read it when I found DS' behaviour really challenging at the start of the year, and I found it really helpful in still addressing some behaviours but in a different way that doesn't escalate into a row/tears. DH said he would read it too but he downloaded it on his kindle about 6 months ago and hasn't got very far.
Sorry, this is so long but if you've stuck with me, the AIBU is that I'm at the point now where I'm fed up and will call DH on the behaviour. So this morning the cereal/milk spilling incident happened (we're talking drips of milk spilled, not a bowl's worth) and when DS inevitably got stroppy with DH for making him sit properly and pushing his chair under the table, and DH responded with "don't you dare shout at me..." I told him he should've just ignored it, who cares that he spills a bit of milk. DH then has a go at me for micro managing him, but I only call him out when I see him micro managing DS. This is all in front of DS by the way, I try so hard not to argue in front of him but in lockdown he is almost always there. The only time he's not is bedtime, so I do tend to call things out when I see them.
DS' mood is often affected for the rest of the day then, if there's been shouting from DH and him crying. It's generally me who then has to handle him as I'm working PT. Plus, I don't really want him to be an unhappy child who's constantly picked at.
So AIBU? Should I just bite my tongue, walk away?
I'm really interested to hear about what others do when it comes to co-parenting.