Am I Obligated To Pay My Ex “back” For Mortgage Payements And Utilities (both On Deed) When I Was Not Living In The House But They Were?

I have just sold a home I co-owned (both on deed, both on the mortgage) with my ex. I left because of abuse and isolation, keeping me from my child even in the same home, June 1st last year. I got an apartment very nearby to co-parent our child (who my ex is currently trying to have fully removed from me in court, and is losing that case badly so is very angry it turns out you can’t have a baby with someone then just walk away!!!). After I moved out, we had a verbal agreement I would pay “less” in mortgage payment since my ex and child were living in the house so we wouldn’t sell right away and I was paying for rent elsewhere as well.
I paid approximately 2/3 of my part of the mortgage payment every month since, and the water bill every month. But not the other utilities. I realized after the fact technically I also didn’t pay my 1/2 of the car insurance bill monthly as it was coming out of our joint account.
We have now sold and my ex is demanding the “back pay” from the mortgage I didn’t pay, and thousands more for my “half” of the utilities. Note: I am the significantly lower wage earner.
When my ex threatened to stop the sale of the house after we had an amazing offer over this I stupidly appeased them (on the dumb advice of my parents) and said ok I’d pay back just the mortgage at 4k which is what I caluclated was the difference between excatly 1/2 and what I paid. They allowed the sale to go through, but sent an email 5 minutes before signing for closing demanting much more. At this point I don’t even want to give them the 4k. Am I obligated to pay fully 1/2 of the mortgage when I wasn’t living there and my ex was (it was a 4 bed 4 bath house in an amazing neighborhood, I was living in a small studio above a garage to afford paying the motgage and rent and now the fact I was living there is being used against me in custody court saying I didn’t have a suitable home for our child)? Am I obligated to pay for utilities and /or home insurance during that time? What about the month the house was empty between sale and closing? Also my ex seriously delayed the sale of the house at one point over just not wanting “dust” with a contractor doing minimal but necessary work while they were living there.
Also note: After we signed an agreement to buy the house 4 years ago, I personally negotiated including a gorgeous baby grand piano in closing because I knew the seller, had known their child who is also a musician, and am a degreed classical musician myself. When we split up, my ex and I also verbally agreed I’d take the piano. Then in the same email demanding 4k for back mortgage, my ex said the piano was 1/2 hers since it came with the house and so I either had to pay 1/2 of its assessed value (20k) or sell it and give her half the money (impossible - no one buys grand pianos), or pay to have it destroyed. Basically: if I wanted my piano, I had to pay her 10k. I ultimately agreed to include it in the sale which we did but I’m devestated - I loved that piano. The only reason we had it anyway was ME and my approaching the seller.
I can’t let this person steal any more from me, but I know I need to honor my obligations.
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