Split with partner
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Tbh I have no personal experience in separation with a child involved but I’ve been with someone with similar mental health issues and well done for getting yourself out of there, it’s very easy to stay and let them become narcissistic. Get some real legal advice, there are a lot of free service out there, however all my friends who have gone through separations involving children the “courts always favour the mum”, in some cases that isn’t always the best outcome, but by the sound of things your a very responsible caring parent and sounds like you’ve been the primary caring for child the last two years. I hope this gives you a bit peace of mind and gets resolved without too much aggro. X
Are you expressing a query about concerns on his mental health and ability to take care of the kids? Does it sound like he won't negotiate about the shared parenting? How is he with the kids in general and does his mental health impact his ability to parent and safety? If all the answers are negative maybe seek a family solicitor or try a free advice line like gingerbread for some advice.
If you can evidence and document his mental health then it's highly doubtful at least until his had some intervention with his mental health. I'm in a similar position but what I identified as mental health issues he believes are cultural differences. I beg to differ! He wants the 1 week off/on divide also but we are not going through any legal formalities yet.
You could try coming to an agreement yourselves - eg suggest 1/2 nights per week or day time contact only if you’re comfortable with that. If you don’t come to an agreement amongst yourselves, your partner will likely have to submit an application to the courts for a child arrangement order. The court will usually hear from both parties, and if you disclose the concerns (as mentioned above) with evidence (anything you have, plus a CAFCASS officer may be assigned to you and will interview you both / see how LO is, etc) for the safety of your LO, then the judge will make a decision accordingly.