IMO absolutely not - and yes it is a "stupid" idea to consider at this time unless you don't really care about seeing the kids.
She will bring them to you ? Does that mean you take them back every other weekend ? Or is she going to stay in town and drive them back the next afternoon ? That is 7 hours round trip.... If she takes them both ways she's basically driving the entire weekend. That's a lot of gas that's expensive these days and her whole weekend. Two little kids would be in the car 7 plus hours every other weekend - hardly a joy for anyone - and IMHO really unfair and crappy to the kids. You'll get them about noon or later on Saturday and if you have to take them back you'll basically need to leave at 2 on Sunday to make it back by 9 or 10 that night.
My prediction is this arrangement will end up very short lived. If you let her move now with permission I think you can basically say goodby to your kids and being a dad till their at least teens. Even if the transportation arrangement is in the settlement, once the divorce is final if she changes her mind your pretty much SOL and won't be able to do much about it in reality besides sue for a change in custody which you'll have little chance of because you agreed to this. If that's cool with you then fine - let her move. But no poor me I miss my kids and want to be their father later - your volunteering. Also realize the new guy will basically become your kids dad.
If you want a clean no strings break besides sending a check this way will probably work. If you don't I think you better say no - emphatically.