Does My Stepdaughters Dead-beat Mom Have A Chance At Winning Her Case?

My stepdaughter's mother deserted her in our home state in our care and moved one state away in 2023 and has maybe seen her five times in a year and a half. Before this we had her weekends and every break until September of 2023 when we had her full time when her mom left. We claimed her on our taxes filing for 2023. In their parenting plan it states that they have to alternate years on who claims the child. We also claimed her this year because her mom has seen her around 15 days total out of the whole year and has given us about $60 towards care of the child. The mom is threatening to take us to court over this because it was technically her year to claim her according to the parenting plan. In the parenting plan it also has us having her weekends and breaks and the mom throughout the week which is obviously not happening. It also states that no parent can move more than 50 miles away, which she did. My question is, will she have a case when we have had her more than 50% of the time for the past two years and she has not followed the parenting plan?