Don't do it. Tell they you love them dearly, but you don't have any baby skills to fall back on.
A friend had to go back east to deal with a custody issue of her two girls. We had the girls for 2 1/2 weeks. It's been 13 years since we had anyone that age in our home for any length of time. And we only had one child. These girls were 8 & 9 and were fairly self reliant but still, it was a LOT of work. A six month old baby? They are NOT self reliant. They cannot tell you anything. They make a series of noises that you use to guess the issue and then, by process of elimination, work to figure it out. But sometimes there is NO answer. If you were closer to them (geographically) and knew more about the baby's day to day, hour by hour, routine it might work. Since that isn't the case and they want to add in the crazy mom I'd tell them you'll tied up with work, out of town, kidnapped by aliens, hospitalized having plastic surgery, witnessed a mob hit and going into witness protection ...