for dns, you want to add a cname for www.domain2.com that points to www.domain.com (or add a identical A value) and do the same with domain2.com (without the www)
Next, on your website, You need to allow it to answer for domain2.com but I can not give you much help as this will change depending on what host you use as nearly everyone has a different way to do things (unless using the same panels!)
Check on the hosters specification if it says how many domains you can host on the account, if it only says 1, they will most likely block it, however if you are having trouble and it says more than one, email them and they should help.
Also if they won't help you and still having problems, you can use a free service such as www.everydns.net as your nameserver / dns provider and get them to forward all traffic (Can't remember if it is redirection or through an iframe) to www.domain1.com