I advise on benefits and other things. Unfortunately you've had a lot of incorrect advice on this thread. You should contact Citizens Advice, either your local branch or the national helpline - see www.citizensadvice.org.uk/about-us/contact-us/contact-us/contact-us/
They should confirm everything I'm about to tell you.
First things first, you can and should claim new-style JSA, which is not means-tested (so your BTL property is not relevant). Eligibility is based on National Insurance contributions, so if you worked and paid NI in the tax years 2018-19 and 2019-20, you're eligible. It's only £74.35/week but it's better than nothing. Info and link to claim at www.gov.uk/jobseekers-allowance
JSA won't solve your housing issue, of course. You can't claim Universal Credit while you own a BTL property that you don't live in; both the equity and the income from the property disqualify you (assuming they're above the limits, which is likely). So I think your best course of action would be to give the tenants notice to leave and to continue living with your ex until they do, if that's possible (it could be a long time!) Do the tenants have a fixed term tenancy or periodic? If you're using a lettings agent they should be able to advise but there is also info at www.gov.uk/tenancy-agreements-a-guide-for-landlords/ending-a-tenancy
Once you move into the property you will be able to claim Universal Credit (assuming you meet the eligibility criteria) but it won't include any contribution to your mortgage, but you could apply for an SMI (Support for Mortgage Interest) loan if and when you become eligible. See www.citizensadvice.org.uk/benefits/support-for-mortgage-interest-smi/support-for-mortgage-interest-smi/deciding-if-you-should-apply-for-smi/
Also bear in mind that after you move out, your ex will need to pay you child maintenance.
Did you get a redundancy payment?
Hopefully you'll find a new job, but even if you do, I would still advise ending the tenancy so you can move back into your property - or sell it if you want. If you do put it on the market, it will be disregarded for benefits purposes for a certain length of time (26 weeks off the top of my head but I'd need to look it up to be sure).