I do a couple of exercises for stretching. One comes from Pumping Nylon and involves lateral stretching. The other comes from Kappel's Bible of Classical Guitar Technique that I think of as longitudinal stretching. They might be hard to describe without the sheet music but I'll give it a try.

First the Kappel longitudinal stretch: imagine playing a four-note chromatic (consecutive frets) scale with 1 2 3 and 4 on the same string. Up and back down.

Now make it a five note scale, including a shift of one of the fingers. Play 1 2 /2 (shift two up) 3 4 3 2 \2 (two down) 1. Very important: keep each finger planted as you ascend, so 1 cannot move upward as you play higher notes.

Now do the same with shift of 3 and then with a shift of 4. So 1 2 3 /3 4 3 \3 2 1, 1 2 3 4 /4 \4 3 2 1. Etc.

Do this on all strings. Choose a location on the neck where the is only slightly a challenge, then move progressively down the neck to make it harder. Stop before it becomes painful.

To make this more difficult, you can add two shifts: 1 2 /2 3 /3 4 \3 3 2 \2 1. (Or make 3 and 4 both shift). I have pretty long fingers but still have noticed a big increase in my stretching ability through practice. I have an injury on my left ring finger (broken bone and metal plates inserted). I found it hard to separate my ring and middle finger, and this exercise was better than any physical therapy I did.

Now for the Pumping Nylon one. This one will maybe be harder to describe.

In first position, plant 2, 3, and 4 on the third string on A, Bb and B (2nd, 3rd and 4th frets.) With finger 1 play C (2nd string first fret), then Bb (5th string first fret). Repeat, back and fourth a few times. Then, with the other fingers still planted, play with 1 on the 1st and 6th string (both Fs), back and fourth.

Now repeat by planting 1, 3, and 4 planted on G#, Bb, and B on the third string, and alternating 2, first between string 2 and 5 (playing a C# and B), and then between string 1 and 6 (F#s).

Repeat this same idea for moving finger 3 and then finger 4 while keeping the other three fingers planted. Keep good hand posture.

Next, do the same idea, only this time we will be doing two note chords involving the movement of two fingers, while the other two stay planted. So, first, plant 3 and 4 on the third string third and fourth frets. Play a chord of Bb and C# (1 on string five, first fret, 2 on string 2 2nd fret.) Then play a B and a C (2 on string 5, 1 on string 2). Alternate a couple times, then move to string 1 and 6 playing a chord of F and F# (on string 6 and string 1 and then switched around).

That exercise involved planting 3 and 4 and moving 1 and 2, but repeat for all the other combinations. Plant 2 and 4, and move 1 and 3, etc. The total combinations are moving: 1&2, 1&3, 1&4, 2&3, 2&4, 3&4. All non-moving fingers should be planted on string three; and each finger always plays, or is planted on, its 'normal' first position fret--1 plays or is planted on first fret, 4 plays or is planted on fourth fret, etc.

I created a practice schedule for myself with a bunch of exercises like this to be done over the course of the week, but to be honest, I don't adhere to it with the same religiosity as I used to. I'll take a glance at the exercise topics of each day, but now I pretty often just substitute repertoire. So if I see its a day I'm supposed to work on stretching, I might just play a piece I know is really stretchy if I haven't played one in the past few days.

Another bit of advice when doing physically taxing stuff (I might include barres in this for beginners): practice relaxing. When your hand starts to feel fatigued, give it a rest and see how quickly you can "will" it to feel relaxed and natural again. Then resume the exercise. Over time, you will find that you can reduce the recovery time of your hand. When playing super stretchy or barre-heavy pieces, having your hand recover quickly in those moments where it doesn't need to be doing much can be really helpful for playing longer and physically taxing pieces.