Hello. I'll be happy to assist you.
No, that does not make you exposed to an abandonment charge. For a parent to abandon a child, they must exhibit some intention to not return for the child or provide any care for them. Taking a job thats out of town, which will cause some physical separation for a few months is not abandonment. You should take every chance you can between now and then to see the kids, even if it's only by phone, and then seek to get them as soon as school is out and you are settled.
Since you currently live in Hamilton County, you will need to file there. You don't have residency in Allen County yet, so it is not a proper place to file. You have to live in the county for three months before you can claim residency there. So, unless you want to wait until this summer to file, you'll have to do it in Hamilton County.
As far as the lease is concerned, there really is no reason to remove your name at this point. He'll probably use that to argue that you never intended to return. Also, the landlory probably won't let you remove your name until the lease is up anyway. Either way, there really isn't a good reason to take your name off.
My suggestion is that you hire a lawyer as soon as you can and try to file for divorce before you move. If that's not feasable, it's not a huge deal, but you still want to start the process sooner rather than later.