Yes it can be done easily (usually anyway), but there may always be that 1 which won't play nice, just rip your DVD, convert it to the format you need, then burn it to a fresh disk, needless to say if it's your 1st venture it will seem overwhelming, but with the right tool it's just a matter of making a few right clicks.
Get Free Studio and install it, it has many tools and should do what you need easily, just click on the logical buttons for what you want, and it will guide you through offering all related options from what you have selected, down to the point you get a program launched and ready to do what you need, the Green button is for DVD & Video, then the 1st option is a converter, just check all the settings are right for your country (NTSC, as opposed to PAL which is UK, whenever your use something with such an option), or try the 2 Orange buttons instead, see how you go.
Important Note; I hate any page that pushes stuff at you, and unfortunately this site now seems to do it as well, so if needed use the Esc (escape) button to clear the pop up window that obscures the page, and ignore anything else that comes up.
But the software you used to make your disks originally are supposed to be able to do what you want, Here is a guide on the subject which may help with that if you want to stick with what you know.
But generally speaking the format you need to use can be one of a few, depending on the quality you want at times (I'm guessing here), but the restricting factor is the player it goes in, players are usually capable of reading several formats, but this varies, often a lot and usually reflected in the price of the player, but generally speaking I believe the MPEG2 format is pretty much playable by anything as best I could see, but others may know better, hope this helps anyway.