The first and probably easiest solution would be to use a cloud service from one of the many providers available e.g., Google Drive, iCloud, OneDrive, Amazon Drive and so forth. There are different pricing schemes, sharing options etc. and I would suggest you compare the available options and choose one that fits best for you and your family. By using such a cloud service, you benefit from a relatively easy setup process and already incorporated remote sharing. The downside is that you lose control over your files once they are uploaded to the cloud, from a data protection and privacy sense. You never truly know how your data is being handled and might also get caught up within a breach of your cloud service provider.
Alternatively, you may also consider setting up a small home server or a NAS (Network-attached Storage). There are many options for customers to choose from, depending on their technological know-how and how much control they want, although at least some technological know-how is required to properly set one up. These enable you to have a home shared drive as well as public ones. This can again be achieved with the right know-how or services provided by the manufacturer. Overall, they are more costly initially and more difficult to set up, but enable you to take control of your data, how it is accessed, who can actually view and edit it, track data access and much more.
As was already stated in the problem description, I would again check the positioning of the router. Are there any objects, big or small, in the way of the signal going to the second upper floor? Such objects could interfere with the signal strength. Think of the Wi-Fi signal as beams of light originating from your router that get reflected on each surface until they finally reach your PC or laptop and try to optimize it that way.
Furthermore, you can check your router’s settings for it’s channel settings. To prevent interference from your neighbours Wi-Fi sources the channel settings should be set to “Auto”. You can also try to set it manually, but I would recommend scanning all for Wi-Fis beforehand, with an app like Wifi-Analyzer.
There are also hardware options if you are willing to further invest into better Wi-Fi coverage. Simple Wi-Fi extenders like this one can be placed around your flat to amplify your signal by placing them at key points, e.g. near the stairs where signal might still be acceptable. Also, there are Power-line adapters that modulate your internet communication onto your power lines within your home. These can be hit and miss and depend on your home’s power lines.
The answer to this problem is very simple. Firste, you could try to refresh the web browser. If the problem continues, try to connect with another network. If the problem persist, is better to wait to another moment in which less people are connected.