I, too, have had very little encouragement from family with my songwriting. Both of my kids play guitar, bass, but neither is all that interested in what I write. No wife or girlfriend ever provided me with much encouragement or enthusiasm with maybe one exception. And still, I struggle onward.
Writing is a lonely endeavor to be sure. And although I know a lot of good songwriters I just never have been able to co-write successfully. I seem to need to "surround" a song idea before I can write. Now, given a good song idea I can usually run with it: Joanne Cooper came up with the story for "Heather and Juniper" (see the User Showcase for more info) and I wrote the lyrics in about 30 minutes. But generally the actual writing process has always been a solitary endeavor for me. Oh, I can co-produce with others once the songwriting is done easily enough. But that beginning process is never easy. I always remember a James Taylor quote regarding his own songwriting challenges: "It doesn't come often, and it doesn't come easy." I found that statement encouraging in a defiant sort of way. So I struggle onward.
Songwriting motivation can come from some unusual places. Several years ago I produced an audiobook for Audible (now owned by Amazon.com) for a client, my first introduction to the literary writing world. Later I produced (it's called editing in the book world) two printed books for the same client. As with most NEW endeavors I became interested enough to want to try writing. I wrote and published one book ("The Songsmith"...imagine that) and an audiobook, and am well on the way in a second book. The point is literary writing really gave me some new insights to apply to songwriting. Particularly, I started writing a short, very short, story about whatever song I wanted to write. The process made me really focus on the foundation of my songwriting and actually made the process of starting a song a lot easier. If the short story sucks...I don't honor it with hours of lyric writing, and hours of studio work. I look for another idea. Songwriting is the "instant gratification" endeavor of the creative world in my experience. A novel takes months to write, mine took three, and a daily commitment to writing for an hour or more. While, on a good day, I've come up with a song idea in the morning and had a fairly good finished demo by day's end. By the way, only BIAB will let you do something like that. Another subject altogether.
I think all songwriting methods are valid if they work for you. But keeping yourself up and in the game requires a least a bit of dedication to the art/science of songwriting. READ about songwriting, build a little library of how-to books, listen to a lot of music, especially singer-songwriter stuff. Go listen to some live music. Luckily we have tons of that around Denver and Boulder, and a famous songwriting school in Lyons in the summer. Find what really motivates you and hit that button till you wear it out. And finally, THINK about what you want to write. Don't just throw junk at the wall to see what sticks. Be incisive and thoughtful about your songwriting. If you don't love the song idea you come up with, at least in my experience, you won't find the motivation to give it your best efforts. Done right, songwiting is hard work. It's a lonely experience mostly. "It doesn't come often, and it doesn't come easy."