When to sell property to fund interstate buying?

Hi Forum,

I am a long time lurker and have read and searched everything on the forum that i can that relates to my scenario but i would really appreciate any advice / input.

My question relates to selling a PPOR which is now an IP, to help me buy a home or, add me to a title deed / loan docs and draw equity out from this property instead.

My mother has a family home that has a $350k mortgage on it. Bought in 2010 for $415k it has recently been valued at $800-$850k range. It’s currently rented out for $520pw with long term tenants.
It’s located on the Central Coast NSW, 53km north of Sydney 4km from Gosford Station and 6km from Terrigal Beach.
She is the only person on the title deed and is currently unemployed living overseas.

She wants to help me get into the property market as I’m living in Melbourne and renting. Initially we had the idea of selling the house to gift me the funds to buy house and land package here in Mernda 25km North of Melbourne, then pay down most of the mortgage with the funds to access equity to purchase IP’s in Melbourne or Brisbane.
But isn’t it better to hold than sell properties? And I’m not too keen on the CGT implications from selling the Central Coast home, with only my potential FHOG to soften the blow.

Would it be best to keep the home, put me on the loan docs as a second borrower or perhaps on the title so that the banks will allow drawing of equity? I am fulltime employed $70k per year and my mother is unemployed.
Is this even possible? Or will stamp duty apply by adding me to the title or loan docs?

What doesn’t help is that I have business debt of $15-20k tied up in loans and credit cards and banks will probably look at this as well if going down the avenue of keeping the house and trying to add me on. Also, if im able to get onto the loan docs or title deed for the property, will that impact me going forward for FHOG if I am to fund my first home in Melbourne?

Another thing to note is that as my mother is overseas retired with this IP here and no longer working its quite stressful to have an mortgaged IP that could become vacant at any time which is also a reason we thought of selling or putting myself on the loan / title and trying to discharge her off.

I appreciate any thoughts and opinions in advanced.