Walaikum salaam wrt wbt,
From what I've learned your fasts are separate from your prayers. They are two different acts of worship and one does not affect the other's "validness".
About not praying, most say if a person doesn't pray out of lazyness it doesn't take them outside the fold of Islam. It's only when they believe "you don't have to pray" or that it's not a pillar of Islam, then it can take you out.
It's a good idea to check these with your shaikh iA and Allah knows best.
(Some more details: http://qa.sunnipath.com/issue_view.asp?HD=1&ID=12887&CATE=239
That said, not praying is still a major sin. It's considered the 4th major sin!! Right after shirk and murder and stuff! And 5 xs a day for years really adds up!! Do they really want to accrue all those sins? What are they going to say when they meet Allah?
Maybe you can read some articles or watch some lectures on youtube on the seriousness of abandoning prayer and reiterate these to your family as best you can. Keep bringing it up every so often, just a point here and there and leave it at that. Don't hound or lecture too much. People's own feelings of guilt and consciousness will come up iA. Also you don't want to make that link of not praying/not being muslim because ppl may abandon islam altogether and you don't want that!!
Also maybe discuss with them WHY they don't pray. Some ppl have some very weird ideas when you ask them why they don't do something, then you can refute their ideas iA.
Good luck inshaAllah.