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Possible workarounds:

• Substitute what you want to be simplified in the original (larger) expression containing the (unspecified) pther factors (not shown in your exemples...), possibly helped by use of wildcard patterns.

Examples

sage: reset()
sage: from sage.manifolds.utilities import simplify_chain_real
sage: w0, w1=(SR.wild(u) for u in (0, 1))
sage: p1,p2,p3 = var('p1 p2 p3', domain="positive")
sage: ER = p1*p2*sqrt(p3)*sqrt(p3/p1)*sqrt(p3/p2)/((p1 - p3)*(p2 - p3)*(p3 - 1))
sage: E1, E2=var("E1, E2")
sage: E=E1*(E2+ER)
sage: E.subs(ER==simplify_chain_real(ER))
-(sqrt(p1)*sqrt(p2)*p3^(3/2)/((p1 + p2 + 1)*p3^2 - p3^3 + p1*p2 - ((p1 + 1)*p2 + p1)*p3) - E2)*E1
sage: E.subs(w0*(w1+ER)==w0*(w1+simplify_chain_real(ER)))
-(sqrt(p1)*sqrt(p2)*p3^(3/2)/((p1 + p2 + 1)*p3^2 - p3^3 + p1*p2 - ((p1 + 1)*p2 + p1)*p3) - E2)*E1

• Specify exactly the subexpression(s) you want simplified via Maxima's part and subspart functions (available via the maxima_methods() objects).

@eric_g: shouldn't simplify_chain_real (and, better, a similarly named method for SR elements) be part of the standard code of SR ?