It sounds like you may not be too experienced with a soldering iron.
If thats the case maybe practise desoldering on an old videogame pcb first ( they are cheap & easy to find) rather than hack up the existing board.
Otherwise do as Dean said, cut the ic pins ( A Dremel tool with cutting disc is handy for this ) and probably what I would do is solder your ic soket pins to the bits of old ic leg that are still poking thru the board because that way you will be able to put a good blob of solder on each one.
If you do desolder the whole thing you really do need some desolder wick too ( from Jaycar) to clean up the holes so the ic legs will go thru. But do be careful because too much heat will lift the pcb track off the board.
It should be worth noting that 5101s are a CMOS device and as such you should wear an anti static earth strap when you solder it in.
Anyway good luck with it and let us know how you get on.
