Creative way to move in together and use current properties

[Luis Gabriel Vargas]

My girlfriend has a house with about $500k in equity and divorced a few years ago. The house in under her name but the ex is paying a portion of the mortgage because she has the kids and he is the one in the mortgage. My property only has $140K in equity but I don't have any other debts, she of course is paying about $800 a month for her pretty car. I proposed to put down 20% (50/50) on a house where we can live together and invest the rest on other properties since she said she does not want to live in a house that is only mine...I won't ask why. I had another idea of her getting a HELOC and use only the necessary for the 20% of the property where we would live together and rent out the house which according to Bigger Pockets' report will be in the low $3K to cover both the mortgage and the HELOC. I do not want to rent out my condo because the HOA would eat any potential positive cashflow so I am decided to sell it. I am new to this so I am running out of ideas but in reality to start living together we need a 4 bd house for our 3 kids and a bunch of pets so we know it would be a house around $800K until we can make more money from our jobs and side hustles. Can anybody suggest something smarter than my ideas of a complete beginner? I am crazy rolling in bed every night trying to find a way out.