I live in a farmhouse that was built in 1890. We ripped the carpet up after purchasing our home and the hardwoods were in okay shape- but not great. We painted them a distressed white a few years ago and have loved he look, but with a dog and three kids we are looking to install laminate. This is where our problem comes up...One of our living rooms has what we are told are called springboard floors, where the flooring is installed in a rectangle “picture frame” along the edges like maybe 6 boards deep and the middle boards are all ran long ways. There is a slant from the edges towards the middle boards all the way around. I’m trying to do research on how we could install laminate over them without them breaking from having too much give but I’m unable to find anything online referring to “springboard floors” any ideas?!

A floor with a border usually has a sub-floor. Do you have a sub-floor under the floor with a border? If there is a sub-floor you will have no problem laying another floor over the top of the existing, strength-wise.
You will need to flatten the existing floor with something so that you will be within tolerance of the instructions for laying your flooring if you want to have a warranty
Use a straight-edge to see how much you need to raise the middle of the room, which is called the field.
If you do not have a sub-floor, you can either add blocking between the joists or add another u underpayment on top of your finish floor that you have, now.