If custodial parent dies and live with grandparent, does the grandparent get custody over the non-custodial parent?

This is my first time writing something like this, so please bear with me. I have 3 children by the same woman, in 2 different counties in Ohio, because we moved while she was pregnant, we lived together, but were never married. My name is on their birth certificate hyphenated with hers, and there is a child support order in place which I know means nothing, but when we stopped seeing each other I had asked to get visitation rights, and she went all crazy stating that where live is not a safe environment, I don't know how to take care of them, etc. Since the break up in they all stay with her parents,(kids grandparents) About a year ago she finally started giving me the kids over night, then weekly, and now at times, she would make excuses why she can’t pick them up on dates we agreed on. Lately I've noticed that she has lost a lot of weight, and has very low energy, overall looks bad, I ask and she says she's ok, we only communicate via text, and I have noticed that she been trying to BAIT me with questions that would make me mad, a lot of them read as follows, my mom does everything for these kids, your mom doesn't do bleep, my mom spends thousands on these kids, you and your mother don't do bleep and so on. In the beginning of our break up my mother, and I both gave her money to her, NOT child support, because she needed it right away, I gave her my car, for her and the kids, then it died so my mother gave her, her car. Now I have had 3 brain surgeries since, and I am on disability, and cannot work, the kids still get child support plus dependent benefits because of my disability, we live an 1 1/2 west of her, she is the one who always brought me the kids, and picked them up because I cannot drive anymore, and its hard for me to find transportation. so can she cut me out and give custody to the grandparents, also could she drop my last name that is hyphenated with hers on the kids birth certificate for their school, etc.