To remove those cups tap them out from the opposite side with a hammer and an expendable screwdriver.

To install a 3 piece bottom bracket check out BMX sources. You can either instll a BMX 3 piece crankset or you can press inl an adapter which will allow you to fit a Euro bottom bracket and crankset.

Either way you'll be spending quite a bit of money on a rusty old frame. A much cheaper solution would be to fit an appropriately sized chainring to your existing 1 piece crankset.