Arizona Rules of Civil Procedure 4.1states in pertinent part:

(d) Service of Summons Upon Individuals. Service upon an individual from whom a waiver has not been obtained and filed, other than those specified in paragraphs (e), (f) and (g) of this Rule 4.1, shall be effected by delivering a copy of the summons and of the pleading to that individual personally or by leaving copies thereof at that individual's dwelling house or usual place of abode with some person of suitable age and discretion then residing therein or by delivering a copy of the summons and of the pleading to an agent authorized by appointment or by law to receive service of process.

From the rule, papers can be properly served by leaving "leaving copies thereof at that individual's dwelling house or usual place of abode with some person of suitable age and discretion then residing therein."

Therefore, there appears to be two issues to be challenged. First, since the person alleged to be served was a babysitter, there an issue to be argued that said person does not "reside" in the home. Also you could challenge that the babysitter, due to her age, was not a person "of suitable age and discretion." This argument would most likely fail though.

So you can either choose to file a response within the 20 day period of which case you will submit to service and the case would move forward. In the alternative, you can do nothing, wait for a default hearing to be set on the matter and then argue to the court at that time the reasons why you were not properly served. In the latter case, if the court determines that service was proper, then you run the risk of having the court enter judgment against you for failing to respond in a timely manner.

I hope this was of assistance. If you desire further advice, please feel free to call our Firm to set up a free consultation.