This all sounds very familiar to the arguments my partner and I had at this stage of parenting (ours are a little older now). Every couple's path through it is different. I found it hard, as a Dad, when I did help, but my "way" with the baby was different and didn't instantly work and got met with negativity both from mother and child (who both have much more confidence in each other). The way we got it to work was to create space. So, if my partner needed a rest, I would take baby out for a few hours / the afternoon / whole day. Or, my partner would go out for a few hours / the afternoon / whole day. I learnt quicker and got better and built confidence and my partner got a proper break (from all of us!). I understand this approach is tougher in lockdown / bad weather but there's always a way. Just an idea. Good luck. It will get better.