Split it. But not all!

R, 34 bytes

Regular unmodified scan with the appropriate arguments for text, sep and quote should do it.

function(D,I,S)scan(,t=S,"",,,D,I)

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C (gcc), 64 bytes

c;f(d,i,s)char*s;{for(;*s;s++)*s==i?c=!c:putchar(d-*s|c?*s:10);}

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JavaScript (Node.js), 57 bytes

(d,i,s)=>s.replace(c=/./g,e=>i==e?(c^=1,''):d!=e|c?e:`
`)

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Pip, 18 bytes

FxcxQb?!:oOo?xRanx

Takes inputs as command-line arguments. Try it online!

Completely different approach: process the string one character at a time and output the desired results newline-delimited.

How?

                    a,b,c are cmdline args (respectively representing D,I,S); o is 1;
                    n is newline (implicit)
                    We use o for a flag indicating whether or not to change D into newline
Fxc                 For each character x in c:
   xQb?              If x equals b (the ignore character),
       !:o            Logically negate o in-place
          O          Else, output the following (with no trailing newline):
           o?         If o is truthy,
             xRan      x, with a (the delimiter) replaced with newline
                 x    Else, x unchanged