TI-BASIC (TI-83 Plus), 32 bytes

Input G
Input S
Input U
Input L
{0
While G≠sum(Ans
randInt(U,L,S
End
Ans

Can take a while for inputs that have only a few possible outputs, but it works

Wolfram Language (Mathematica), 49 47 45 bytes

RandomChoice@*GroupBy[Range@##2~Tuples~#,Tr]&

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Input [SplitCount, LowerLimit, UpperLimit][GrandTotal].

Charcoal, 34 bytes

ＮθＮηＮζ≔⊕⁻ＮζεＩ‽ΦＥＸεη⁺﹪÷ιＸε…⁰ηεζ⁼Σιθ

Try it online! Link is to verbose version of code. Takes input in the order GrandTotal, SplitCount, LowerLimit, UpperLimit. Explanation:

ＮθＮηＮζ

Input the grand total, split count and lower limit.

≔⊕⁻Ｎζε

Input the upper limit and calculate the length of the inclusive range from the lower limit to the upper limit.

Ｉ‽ΦＥＸεη⁺﹪÷ιＸε…⁰ηεζ⁼Σιθ

Generate the Cartesian product of the split count number of inclusive ranges, filter out those whose sum isn't the desired grand total, and output one uniformly at random.

Python 3.8 (pre-release), 116 bytes

-12 bytes thanks to Jitse

Accepts input in the form of GrandTotal,SplitCount,UpperLimit,LowerLimit.
Returns a randomly picked range, as a tuple, from a list of possible ranges.

lambda g,s,u,l:r.choice([p for p in i.product(range(l,u+1),repeat=s)if sum(p)==g])
import random as r,itertools as i

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JavaScript (ES6), 85 bytes

Expects (count, lower, upper)(total).

(n,a,b)=>g=(t,k=n,s=t,...o)=>k?g(t,k-1,s-=q=a-Math.random()*(~b+a)|0,...o,q):s?g(t):o

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(NB: The function is likely to stack overflow on some test cases. The above test includes some extra recovery code.)

Bash, 164 bytes

echo>0
seq 1 $2|xargs -I, sh -c "rm ,;seq $4 $3|xargs -i sh -c \"<\$((,-1)) sed s/^/{}\ />>,\""
<$2 tr \  +|sed s/+$//|bc|pr -mt $2 -|grep $1$|cut -d\	 -f1|shuf -n1

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Burlesque, 49 bytes

r@s1Js2rzjCBf{++g2==}f{{g1j~[}al}sa-.3 0x/rn1.+si

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r@s1          # Range from lowerLimit to upperLimit and save to 1
Js2           # Duplicate grandTotal and save to 2
rz            # Range [0, grandTotal]
jCB           # Combinations of SplitCount
f{++g2==}     # Filter for sum == grantTotal
f{{g1j~[}al}  # Filter for all elements in range
sa-.3 0x/rn   # Generate infinite list of random numbers [0, len)
1.+si         # Take 1 and select it

05AB1E, 8 bytes

ŸIãʒOQ}Ω

Inputs in the order UpperLimit,LowerLimit,SplitCount,GrandTotal.

Try it online or verify all test cases (without the }Ω).

Explanation:

Ÿ       # Take the first two (implicit) inputs and push a list in the range
        # [LowerLimit,UpperLimit]
 Iã     # Create all combinations of a size of the third input SplitCount using
        # the cartesian product
   ʒ    # Filter this list of lists by:
    O   #  Sum the list
     Q  #  Check if it's equal to the fourth (implicit) input GrandTotal
   }Ω   # After the filter: pop and leave a random list
        # (which is output implicitly as result)