Stop walking into walls!

JavaScript (ES6), 192 163 bytes

a=>b=>a[(a[4]=0)+--b]?(A=(c,d)=>c==b|(e=a[c])-(f=a[d])|!e?(a[c-b?(e?e<f:new Date&1)?c:d:4]=2,a):A(+g[c],+h[d]))(+(g="3016X2785")[b],+(h="1250X8367")[b]):(a[b]=2,a)

Notes

This function uses a special input format. The first input is an array of integers (0 for floor, 1 for wall and 2 for player) representing the map. The second input is the (flipped) direction: 1 is north-west, 2 is north, 3 is north-east, 4 is west etc. The inputs should be given through currying syntax (Z(a)(b)).

Test cases

The maps and directions have been modified to suit my input format.

Z=
a=>b=>a[(a[4]=0)+--b]?(A=(c,d)=>c==b|(e=a[c])-(f=a[d])|!e?(a[c-b?(e?e<f:new Date&1)?c:d:4]=2,a):A(+g[c],+h[d]))(+(g="3016X2785")[b],+(h="1250X8367")[b]):(a[b]=2,a)

testcases = [
    [[1,0,0,0,2,1,1,0,1], 3],
    [[1,0,0,0,2,1,1,0,1], 9],
    [[1,1,0,1,2,1,0,0,1], 1],
    [[0,0,0,0,2,0,0,0,0], 5],
    [[1,1,1,1,2,1,1,1,1], 2]
]
for (test of testcases) {
    console.log(Z(test[0])(test[1]))
}

Pyth - 73 70 bytes

Kmsd"78963214"DPGJXXYt@K+xKQG\@4\.R?q/J\#/Y\#Jk=YwV5=GflTmPd(N_N)IGOGB

Try It

Input consists of two lines:

1st line: direction of move

2nd line: The board (positions 123456789, with 123 being the top row)