I'm down with more family-oriented solutions. Paid family leave. Free childcare or credits for it. Cheap medical care. Cheap mental health care. Cheap LTC for seniors. Laws restricting access to weapons for family members. Red flag laws regarding domestic violence. All of that stuff would both help families, which in turn, could potentially curb shootings.
I don't mind red flag laws regarding domestic violence. If you're beating your wife or kids, you've shown a strong propensity to use a gun for evil. No problem with them being taken away.
A law restricting access to guns for family members would be about as enforceable as the sodomy laws were or laws against growing magic mushrooms in your closet. For the most part, you're not going to be able to stop what people do in their own homes.
As for the laundry list of free money, this presumes that a lack of money is what makes families weak. It's not. If it was, then Hollywood would have some of the most stable families in the world. Furthermore, school shootings would have been rampant in the old days when guns were even easier for children to get and bring to school and when welfare programs were less available.
Men don't abandon their children because of a lack of money. Otherwise, rich men wouldn't do it, and poor men always would. They abandon them because of much deeper problems. It's a heart issue, not a money issue (though the heart issue often also causes a lack of money). Furthermore, our culture doesn't judge abandoning your kids very harshly, so there's little downside in doing it. We might say it's it's generally bad, but on an individual level, we shrug it off. A guy in a big city will get a lot more **** thrown his way if he publicly says women don't have penises then if he abandons his kids.
I think the biggest factor in mass shooters seems to be the violence towards women aspect. We don't know why the Vegas shooter did what he did, but for many of the other recent ones (Dayton and El Paso come to mind), they had online activity in the incel community, where idiots on 4chan basically rally around anyone who has the balls to go through with a shooting. The US has only 8% more single-parent families than the UK, so I don't think it's so much a "nuclear family" thing than it is a "online communities got a hold of him" thing.
Agree with your initial premise on the violence against women, but I'd take it more broadly to violence toward the weak. Even if they're not violent to women, they might be violent to children or animals, as Ramos was. They sorta enjoy dominating someone or something living.
The UK comparison warrants some discussion. They have a lot of single parent families (even if fewer than in the US), but the culture here is different. There is a lot more involvement especially by men in clubs and civic organizations.
It's also easier for a guy to build a social circle here. Why? He has a local pub. Seems like I'm making a joke, but I'm not. It's not like a noisy bar in the states that you have to drive 20 minutes to. It's quiet, laid-back, and walking distance from your home. You go in, and within a few minutes people walk up to you and talk to you. Do that long enough, and people get to know you. After awhile, you develop a sense of community, and I think that makes a big difference. It's no substitute for a nuclear family, but I think it definitely helps a lot. You're far less likely to be a loner.
So the lesson from the UK shouldn't be to ban guns. After all, they didn't have a bunch of mass shootings before they banned guns. The lesson is build local pubs in the US.