@FloydWasACat Your life sounds tough. You sound quite isolated. Do you have any support from other family members or good friends? I’d also share this example in the carer’s group, if it feels like a safe space, for their thoughts.
First, if your mother is often abusive, rather than kind and supportive, I’d keep distance from her. If she has concerns about the impact further pets may have on you (money you can’t afford and extra work) or your DH (less money available to the household, physical impact on him of extra pets), she should have had a gentle, humble and kind word with you, showing you she has you and your family’s happiness at heart.
Second, your DH’s behaviour sounds unacceptable. ‘Going apeshit’ (you don’t mention what that consisted of) when you try to discuss getting pets isn’t a mature or respectful response. Telling your mother, presumably aware of how she’d react, is manipulative and undermining.
IMHO, you need to set clear boundaries with both your DH and DM. For your DH, that involves being able to talk to him about your needs and wants and have them considered and, where possible, accommodated with empathy and kindness. And likewise he should be able to do the same with you. There should be a reasoned, mature discussion, with you both looking for compromise, e.g, one more cat rather than two, which is what you had before, so not a big new change.
However, IMHO it was passive aggressive, disrespectful and manipulative to go ahead and apply for two cats when you knew your DH didn’t want that. If your reasonable request for things that give you joy in life (and unlikely to cause problems for your DH) is denied, you should assert yourself and tell him you’ve decided to go ahead and you’ll mitigate the impact on him. Not go behind his back.
But, overall, you need to review how your family dynamics are currently working. Can you access counselling? You need to consider how you can carve out a fulfilling life for yourself in addition to your responsibilities as a carer and earner. Your needs matter. A new cat seems a very reasonable ask. You’re not asking to go on holiday four times a year for a break.
Look after yourself and set boundaries for others. Sending strength ❤️