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It's a nightmare to try and fix these kinds of problems by addressing the cause. Usually you need to observe the exterior during heavy rain at least to see what's happening.
It could be as simple as an overflowing gutter caused by a blockage at the junction with the downpipe but it could be any number of other problems that are difficult to spot and even when you have addressed them it could take months before you know that the interior dampness has been reduced.
Very difficult to fix without properly addressing the exterior problem but there are damp resisting products you can paint on the plaster to stop the damp from penetrating through to the emulsion. It usually has a very high VOC content so you might need to plan around a time when your wife and baby are outdoors and keep the room well ventilated. Then emulsions on top.
Or curtains :)