sprry to hear about your situation. So here is my perspective for what it's worth. Nobody goes to work to do a bad job, sometimes we don't perform because we haven't been given the training or the correct toolset or we don't have the right mindset which could be things going on at home, or with ourselves. Unfortunately it sounds like your manager has gone into proving mode rather than understanding and supporting mode.
I would suggest that you keep notes of all of your conversations with your line manager and have someone accompany you to any meetings. You say "we've" not been Closing cases out properly which suggests it's not just you, I would ask if they are checking everyone's cases and not just yours if this is the case. I would also try and get the situation back under your control, by stating that you are happy to receive feedback and if there is something that you are not doing if they can point it out you will make sure you do it going forward and that you are willing to undertake further training if needed. Also have a think about what will help with your wife and home situation and also put that on the table, I would be open with them about what's going on and needing more flexibility and ask what options are available to you. They should look into what reasonable adjustments they can make at work to enable you to be in work. I would also have a confidential chat with your HR lead about home and that you are looking for support but feel that this isn't forthcoming.
Hope you get it sorted, work is one thing that you don't need to be worrying about at the moment.