Crossing snow field on a regular summer day hike

Have a few hikes in Utah that family does in the springtime.   Trail is typically in good shape, perhaps mud and few patches of snow, but nothing too serious.  However there are 2 or so 20 meter spots of snow fields, that are at a wicked steep angle, and a fall would be very serious.    I've been able to kick in steps, and cross safely, but I'm tired of pressing my luck.   These spots are of great concern, and I want to setup a fixed rope on our way up ( first time crossing ), leave the rope while we summit, cross the snow field on the way back, and retrieve all our gear safely.

These spots are usually North facing ravines, and are narrow in width ( certainly less than 100 feet ) , and greater than a 50 degree angle.   They would have trees to anchor ropes on both sides of the snow field.

Both my boys and I have done a fair amount of top rope rock climbing, all can belay each other,  done a little bit of trad/lead climbing in the gym, been on Rainier ( with guides ), and can certainly pick up any gear for our needs.

So my questions:

What setup would you recommend to anchor the rope on each side?   What methods can I employ on the initial trip across the field to ensure safety?  Once we do have a fixed line anchored on both sides, can we simply harness up, lock into the rope and cross, or is that too simple of methodology?  Methods for getting disassembly of gear?

Lastly, leaving the gear for a few hours while we summit, would you expect the ropes / gear to be left untouched?  Any considerations to worry about with leaving gear in place?

Have you tried using micro-spikes/crampons and an ice axe? Especially if its only for a few short sections of the hike, it seems like that would be more appropriate than bringing up equipment for a fixed line. I would recommend something like a BD raven or Grivel Air Tech, since the patches of snow are so short, you might be able to get away with just using a whippet.

My suggestion is if you and your kids have used crampons and an ice axe and can belay then setup an anchor and belay each other across both ways. You can go first, have the least experienced kid tied into the middle of the rope come across then have the more experienced kid come across tied into the other end.  If the trees are reasonable anchors get webbing and use a girth-hitch around the tree as it can be easily undone (get webbing you tie yourself as there can be tree pitch). If the crossing is significant you might want gear like pickets. Otherwise a fall will result a big pendulum which could dump someone at the bottom and/or side of the snow in the rocks. Before embarking on your next adventure go practice using crampons and ice axe. It will make the crossings more comfortable.

A fixed rope (which is also going to require anchors on both ends)  is not a good idea because others might rely on it and then think it is going to be available on the way back.  When I come down and across fixed ropes they get removed as they are usually abandoned. I have probably hauled six abandoned ropes off of Mt. Olympus over the years.

Are you asking about this year?  Because it's been a miserable year for snow, there's a good chance depending on what mountains you're talking about that there won't be snow on the traverses by the spring, much less the summer.  I did Suicide Chute up the South ridge of Superior with my brother last year (who had never used crampons or climbed a mountain) and with some handy rope-work and ice axe lessons he did fine with no experience.   I digress into Allen's suggestions though, bring a couple of axes and maybe a picket with some cordelette or better yet a little longer rope and just belay the less experienced members across using the rope or cord as an anchor.  Should be standard deal if you understand how to build an anchor and/or do standard snow travel and belay someone.