Ex girlfriend wants to split proceeds on our first house

Hey new to this but about 8years ago when I was 21 my ex girlfriend and I bought a hud home together (mpdu) it’s a first time buyer program no money down needed but there are rules to it, can’t rent out the house, must live in the house. We bought the house for $120,000 about 3-4 years after we bought the house she cheated and we separated, still lived together for about a year and then she moved out took all of her stuff left me with her 3 cats. And I proceeded to pay the mortgage, hoa, insurance, new havc unit. I’ve done some quick calculations and I’ve have spent over $90,000 on the house still owe $99,000 on mortgage, but because it’s a hud home i found it’s more of an anchor cuz I am supposed to stay living there and I’m not aloud to legally rent it out. Recently decided I was goin to sell the house and move on from it with my new girlfriend happy. So I texted my ex gf and told her I was ready to move out but I can’t sell the house unless she signs papers. And so of course she finally responds to me after about a year of me texting her telling her that I would like to sell the house and she ask me “how do I plan on splitting the proceeds” now with a mpdu unit there’s not much Equity so I was told that the selling price that I would get would be about $150000 so I’d have to pay off the 99,000 and then she wants to split the profit of about $40k now the only thing is she didn’t pay for the mortgage,hoa,ect Ever i have all the receipts of me paying for it all. So I ended up having to get a lawyer (cost me $1000 for far) he calls her and she says she’s thinking bout it but thinks she should talk to a few lawyers that was last week Friday, so she called me today and said that she “spoke to a few lawyers and they told her it would be easier for us to just settle it out of court and that they said she should be entitled to 50/50 split. I feel like I have the upper hand for sure I think she doesn’t want to have to pay for an attorney, but in her head she still thinks she entitled to money. Any have any similar situations, what was the outcome and should I just take her to court ?