The 2 Kate Reynolds that appear in Portsmouth in the 1901 census are my GG and G Grandmothers. Kate's husband George Reynolds was also in the army and was not with his family in the 1901 census. Kate is working for Walter Ravish and his family in Sultan Road. Walter Ravish was a witness at the wedding of George and Kate nee Howarth in St Thomas' Church, Portsmouth on 18 Sep 1898.
Have come across a Eleanor Kate Reynolds who was born June q 1902 in Devonport, Devon do you think this could be your Kate Eleanor Reynolds?