If you get no issues pinging the router it means your problem is not in your house. Many people post here with similar issues and it turns out they are using wireless and getting random interference.
Pretty much you call the ISP and complain now. Of course they will say everything is fine.
run a traceroute to some site then open multiple cmd widows and run continue ping to each hop I would do your router too just so you can prove to the ISP it is not your stuff.
When you see a issue see which window the problem first occurs in. If you are lucky it will be in the first couple. The first one will be the connection to your house and likely the easiest for them to fix. The next couple hops will also likely be your ISP equipment and if they have any brains will be able to fix it. The only thing you may find is they have over subscribed something and are out of capacity which is going to be hard to convince them to rectify. Now if the latency spikes are way into the network you can do little this is likely in the interconnections between the ISP and you will never be allowed to talk to anyone who can fix it and you will never get a senior enough person in your ISP so they could escalate it.