OK, given that this sporadic Notifications issue is only limited to your home LAN and that its affecting two different devices that indicates the issue is likely to be with your router.
-- What kind of router do you have? An ISP-supplied modem/router unit or do you have your own, discrete router? If the former, who is your ISP? If the latter, what model router is it?
-- Is distance between either phone and your router a factor when Notifications fail? Do you connect one or both using a 2.4GHz or 5GHz band network? (A very general rule that involves a lot of overlap is a 2.4Ghz band network will have longer effective range, a 5GHz band network more bandwidth.)
-- Is your router physically located in a relatively open spot or is it buried under a desk or something like that? Generally you'll get a better, wider coverage range when it's not tucked in between a bunch of metal file cabinets.
Try installing something like this WiFiAnalyzer (open-source) app:
https://play.google.com/store/apps/details?id=com.vrem.wifianalyzer&hl=en_US
and use it to check your home's WiFi network. It will give you numbers on signal strength so you can walk around your home and get a rough 'heat mapping' on your routers coverage range. It can also give you a better idea on the approximate signal interference from any nearby WiFi networks that could be an issue to address.
