The following configuration is used:

JRE 7 Update 25 is installed in Windows registry.
JRE 6 Update is installed as a private JRE for a Java Web Start application.
The Java Web Start application is started via explicit path,
for example:
C:\jre1.6.0_45\bin\javaws <http-URL>

The JNLP file requires a specific JRE 6 update software version:

<j2se version="1.6.0_45" href="http://java.sun.com/products/autodl/j2se"/>

The 'java 6' splash screen is shown and disappears after a short while.
The javaw.exe process is hung and needs to be killed manually in
Windows Task Manager.

The hanging 'javaw.exe' process is running JRE 7.

Here are the results of a series of experiments:
Everything worked fine with 7u21.
Problems start with 7u25.
The experiments were carried out on 64-bit Windows Vista SP2.
Customer uses 32-bit Windows Vista.

7u21b11 registered + 6u60_b05 private: all fine
7u21b11 registered + 6u51_b11 private: all fine
7u21b11 registered + 6u45_b06 private: all fine
7u21b11 registered + 6u43-b01 private: all fine
7u21b11 registered + 6u21-b07 private: all fine

Beginning with Java SE 7u25 security baseline for Java SE 6
was set to 1.6.0_51:

7u25b17 registered + 6u60_b05 private: all fine
7u25b17 registered + 6u51_b11 private: all fine
7u25b17 registered + 6u45_b06 private: javaw.exe hangs
7u25b17 registered + 6u43-b01 private: javaw.exe hangs
7u25b17 registered + 6u43-b60 private: javaw.exe hangs
7u25b17 registered + 6u21-b07 private: javaw.exe hangs

7u25b32 registered + 6u51_b30 private: all fine
7u25b32 registered + 6u45_b30 private: javaw.exe hangs
7u25b32 registered + 6u43-b30 private: javaw.exe hangs
7u25b32 registered + 6u21-b51 private: javaw.exe hangs

7u40b35 registered + 6u60_b05 private: all fine
7u40b35 registered + 6u51_b11 private: all fine
7u40b35 registered + 6u45_b06 private: javaw.exe hangs
7u40b35 registered + 6u43-b01 private: javaw.exe hangs
7u40b35 registered + 6u21-b07 private: javaw.exe hangs

7u45b04 registered + 6u60_b05 private: all fine
7u45b04 registered + 6u51_b11 private: all fine
7u45b04 registered + 6u45_b06 private: javaw.exe hangs
7u45b04 registered + 6u43-b01 private: javaw.exe hangs
7u45b04 registered + 6u21-b07 private: javaw.exe hangs