re: Is this type of increase in homeowner's insurance common?

The first increase could have just been an accross the class increase.

The second increase is not normal. They had to have made a significant change to the policy - increased limits perhaps - or changed your rating class.

I would not be satisfied with the "we don't know, we'll shop it" line. They (the agent) needs to call the insurer and ask what is going on.

If they are busy, I can see it taking a couple of days to get some quotes and get back to you.

When does the policy renew? I'd call your current agent back and ask them to try harder. If they won't budget, I'd find a new one.