Of course you should look within yourself and do whatever self-improvement you can. You should be doing this for YOURSELF first, and your partner second.
I hope that you guys can follow through on getting counseling, certainly as a couple, and probably individually, too, based upon the kinds of issues you've mentioned here. You will probably learn to be better parents, too, just as a side benefit!

And I'll add my two cents about housework...
I am a SAHM. I'm a great wife in the "romantic partner" sense (loving, attentive), a great parent to our son, and I do a wonderful job managing our finances and investments. (I'm so proud that, staying home, I've managed to create our tiny investment portfolio!) HOWEVER, I'm a really, really poor "housewife". I make efforts to keep on top of the stuff that matters most to DH, but I have never succeeded in keeping a really clean, organized house with more than minimal dinners on the table at the end of the day. I have pretty low physical energy, though my mental/emotional energy is pretty good. We've learned to balance this in our relationship, because, try though I might, I don't believe I could ever be excellent in this one regard. I'm simply not talented in this area.
It might be worth spending time (in therapy?) working out what your DP's priorities and expectations are regarding your "job" in the home, then balancing that with your skills and expectations for yourself.
Some solutions are simple but easy to miss--like my husband is really fine with having salad or fruit for dinner since he eats his main (hot/protein) meal at lunchtime. I was going crazy trying to cook him dinner during my most frazzled, exhausted time of day when all I needed to do was take out a bowl of something I'd washed/prepared earlier! I can't get the whole house picked up, but I can keep DH's favorite chair clear so he can plop into it upon arriving home. I've also learned that DH, like many (most?) men REALLY NEEDS about 20 minutes to decompress upon arriving home before he's ready to hear about my day. (Most women seem to want to talk immediately.) Giving him these few minutes of peace makes his whole evening better.
Good luck, and God bless you both. I really wish you and your family the best in this difficult time.
--willo
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