IMO it is not a simple question, nor does it have a simple answer.
At face value, I would say yes I would leave a 14 year old to care for a 3 month old. But this is not a simple yes or no answer and you know this, despite that being all you asked for.
Here in the US, teens can take the Red Cross Baby Sitter class at age 12. It includes classes on care for babies and kids, including changing diapers, asking parents about food restrictions, first aid and CPR certification. My oldest took it at 12 and started as a babysitter shortly after. She was about 14 when she took care of a baby. Most parents prefer to have older teens who can drive (to the hospital if need be) look after younger kids, but if it is just an evening out and the teens parent is near by it may not matter to them. It is certainly not unusual.
The reason my answer isn't simple is because there are so many factors that need to be considered. Is this 14 year old known well by the parents? Neighbor or family friend maybe? Has the teen been through a CPR/First Aid class? How far away will the parents be and for how long? Is the teens parent nearby and willing to step in if need be? (I myself made sure my kids were not a sitter to far away in case there was an emergency and I needed to step in).
I think the reason why DIL made this choice could answer a lot of questions as well.
My answer to the simple part of a not so simple questions is, yes I would leave a baby with a 14 year old if certain criteria were made.