Hy mrhtbd, if the house has mold, neither you nor your kids should be there. I would not let my kids go spend much time in a building with mold in it. It leads to many many complicated health issues. WTF dude? Why would you buy a house with mold issues? Strong WTF.... Can you get out of the contract? I bet you may be able to.
The first step is to stop the water, then remediate mold from there from there. If you have basement water, there is no half ass approach that will get you to where you want to be: dry. Is water coming in around the footer? If so the drainage pipe around the footer on the outside is probably plugged. Don't think you are going to just seal the walls and correct this problem; water will find a new crack and if it is building up around the footer, which it likely is, it will always leak regardless of how much you seal it. To fix this you need to REDO THE WHOLE FOOTER DRAIN and dig up and remove these pipes/tiles (whatever they are) all the way around the house. Try to dig the trench 24" away from the block wall uniformly and dig it all the way to the footer and scrape the soil off the footer. Remove the existing pipe or tile and throw them over the hill. A small back hoe is your friend here if you have no obstructions, or you may be able to do most of the work with a hoe then shovel around AC lines, gas lines, water lines, etc and whatever.
Once you have a nice clean trench, install corrogated pipe all the way around the house, cutting the pipe and installing 90 deg lbows at the corners. On one corner, run both ends out into the yard, well away from the house to drain away. I dont know what it is called (I called it a pipe condom), it is a nylon mesh cover for such pipe that is designed to keep dirt and mud out of your footer drain.
This will likely correct 90% of most problems by giving the water the same opportunity to drain that any new home constructed would have. To get the other 10%, lets seal the outside of the basement walls. In your case, the most effective and least expensive way to seal the outside of the basement walls is to simply paint them up to ground level with black roof tar, from the base of the wall where it meets the footer all the way up to where the ground will be when you put the dirt back.
Once your pipe is installed and laying against the block wall on top of the footer and your walls are painted with roofing tar and it is dry, cover the pipe with 24" of gravel in the trench. Some people used to put 48" of gravel in the trench but they were likely copying from the tile drain days, but you have a plastic pipe with condom, so not necessary but would hurt. Then backfill your dirt and haul the excess off. Keep some soil to put on after settling to have a level yard.
As you can see this is not a small job.
The roof will need to be replaced before any mold remediation takes place up there. As for the remediation, I would discover exactly what type of mold you have and then go from there. I am sure you can search for the right technique. I had a small section in a finished basement that I remediated through a combination of demolition/replacement and simple chlorine-based bathroom spray. This was a small job. If you got it everywhere, there are commercial products designed for this purpose.
But I will repeat, dont have little kids in a house with mold. They will be sick all the time and for a long time.