Looking for advice

So I went halves on a mortgage with my mum a few years ago, it was a council house so we were able to take advantage of the right to buy scheme. There’s around 30k left to pay off as it stands. I saw this as a good opportunity to get on the property ladder without even having to pay anything. I’m starting to wonder if it was a bad idea or not.

So now, a few years later I have moved into my girlfriend’s flat, she is pregnant and I’m trying to get another mortgage before the child arrives. I’ve got 10% of a roughly average amount needed for said mortgage.

On the first home that is half in my name, I don’t contribute towards the payments as my mum and 2 siblings live in that house and they pay it between them.

Im being told that most mortgage brokers require a 20 to 25% deposit for a second home, which I cannot afford in time for my child.

I’m wondering if it is worth me and my mum remortgaging and getting my name removed, and if this would make me eligible in most places for a 10 percent deposit. Or ideally if it would be possible in any way to get the 10 percent deposit without taking my name off the first mortgage.

Thanks in advance