This is how I'd do it: wget on your local machine triggers a php script on the remote shared host. Essentially, it's just giving you cron. Period.
Then the PHP script on the remote machine triggers the mysqldump. If it's a success, then it sends an email to you with a subject line: "SUCCESS www.domain1.com - mysqldump". If it fails, then it sends an email to you with a subject line: "FAIL www.domain1.com - mysqldump"
That way, you don't have to sit down at your machine to perform the dump. It continues working even when you're on vacation. You could even have the failure emails sent to your cell phone while success goes to your regular mail.
I know it's extra work. It's worth it when it's all done. You'll thank yourself for taking the extra time. I mean, truthfully, you have to write the remote PHP script (which you were going to have in an iFrame) perform the dump and FTP the resulting file somewhere. That's the hard part. Writing a wget cron is one line of code. It's probably 20 mins of work the first time you do it and then 30 seconds for each extra time. You were going to write a page with a bunch of iFrames... that was going to be 20 mins of work anyway. I don't see this as very much harder and it's a good skill to have. Come on, everybody's doing it. 🙂