What type of visa does my aunt need to come to help us with a baby?

Your aunt can visit in the U.S. for up to 90 days at a time two times in a one year period. that year begins on the 1st day of here first visit. Technically, what she was told is not correct...but if they see someone spending a lot of time in the U.s., they sometimes get nervous and bossy about it. and some of those guys are just power hungry little Napoleons. She should be able to re-enter the U.S. with her ESTA clearance if it has now been a full year since the first day of her first visit. Otherwise , she needs to apply for a B-2 tourist visa...which allows her to stay up to 6 months in a one year period. She MUST have proof of compelling reasons to leave when she is supposed to...this means own a home or business or have a lot of money in the bank. About 50% of tourist visa applications are declined. if she were to be declined, she could not then come under the visa waiver program. If she decides to apply for a B-2 visa, she needs to start with the page below.

Quit making slaves out of your relatives and pay a nanny or take your child with you.

Charlie is correct and the Immigration Officers at the airport do not have the power to tell her she has to apply for a visa. However, they do watch for people who try to (illegally) live in the USA using the Visa Waiver Program and multiple long visits are a giant red flag. You don't say when her previous visits happened or how close together they were. If they were in 2011 and her next visit will be in a few months it may not be an issue at all. However, you DON'T want her to be refused entry so talk to the office of your US Representative (Congressman) to see if they can help or provide advice. Ensure she has the documentation required to show her visit is temporary such as a round trip ticket leaving in LESS than 90 days and things like travel medical insurance. Letters from friends/family in the USA usually have no effect on US Immigration but ask the office of your US Representative for wording suggestions. If you do decide a regular tourist visa is needed she needs to talk to a real travel agency in the UK that is familiar with the documentation requirements and you should consider talking to an immigration attorney. As Charlie points out, a high percentage of visa applications are denied (often for no apparent reason) and a denial would cause here problems entering the USA (forever). Remember the reason many people in the world don't like the USA is they way they are treated by Visa Officers at US Embassies & Consulates and then by Immigration Officers at USA airports. (they are treated badly, arbitrarily, and capriciously)