You cannot combine purchases from two different accounts into one account. The apps that your mom bought will always be tied to her ID and you will always have to use her ID and password in order to update those apps. That same rule applies to all purchased content in the iStores on the iPad or in iTunes on your computer.
You will also want to take heed of signing in and out of accounts in order to download past purchases with different Apple ID's. you can lock yourself out of your own ID for 90 days if you are signed into your mom's account in order to download previously purchased content.
Read this for more information.