Eek!
All three of the Nannies have a very important deal-breaker which could seriously become a huge issue for your family if hired.
#1): Caring for a three-month old infant requires a bit of experience since one must know all about feedings, diapering, erratic sleep patterns & calming techniques.
It takes a special kind of patience to care for a young baby and caring for one alongside two other young children can be quite challenging whether one has experience or not.
#2): If this Nanny were so "Professional," I find it clearly odd that you cannot get ahold of any of her former employers.
It also is a huge red flag to me as well.
DO NOT HIRE HER w/out speaking to her former families first!!
It is very important to speak w/her previous families in order to get a first-hand personal account of how she fares around young children.
#3): You would be taking a significant risk if you hired this person.
Your children will become very attached to this woman + it may be tough for them if she ends up finding a full-time position and leaving them.
Plus you will always have some anxiety about whether or not she will be looking for another position behind your back.
If you have the time, I strongly encourage you to keep looking until you find a much better fit for your needs.
If that is not an option however, my choice would be candidate #1.
Good Luck!