Sounds like there’s loads going on here, but the main one is your mental health, I hope you manage to get some help both at home and from the professionals.
I’m a bloke, so take this as you will! The main thing I always think when I read these types of threads (seems there’s lots!) is that I can’t imagine living in a house where the atmosphere must be so strained all the time due to the disparity of effort/work.
For what it’s worth, we have two kids (5&3) and we both work full-time. We both have a night out each week (if we want it), and when we’re in together, we’re normally sat down by 8ish with dinner. The house - by most standards - is pretty neat, clean and tidy, but we accept not everything can always be 100%. The garden is not how we’d want it to be, but it’s lower down the priority list at the moment. We have a cleaner for 2 hours every two weeks for some of the bigger jobs, but other than that it goes…
Weekday Mornings & drop offs - 100% me
weekday pick ups - 80% wife / 20% me
bed, bath, story - 50/50 (we usually divide and conquer)
weekends - 50/50 (usually each have half a day to ourselves to do jobs and a bit of downtime, rest as a family)
GP/dentist/haircuts etc. - 50/50
Buying stuff for kids - 100% wife
food shopping - 100% wife
life admin including finances, school stuff, nursery stuff etc - 60/40 to my wife
cooking - 90% me
day to day cleaning - 70% me, but I work from home most of the time, so factor it in. I do more of the ‘manual’ stuff but wife does the things that make the place feel nice
DIY/gardening etc- 50/50 depending on preference and ability
Life is hectic and a bit stressful- but, I think, it can be done… but only if both people take responsibility & you play to your strengths. It’s also worth proritising what’s most important to you personally though (I hate dirt, but can live with a bit of clutter / disorder… my wife is the opposite, so we both take responsibility for our own happiness/ sanity in those areas)