In something like this, it's probably best to lie- not for the bad, but to keep from hurting someone's feelings.
Just ask your friends that are going not to tell Rachel about the party or to ever mention it.
Also tell Rachel it won't be on.
On another day you could organise something at the beach where your mum won't be around as much and Rachael can come. OR invite Rachael to the party, but say it's not a sleep over. This way, she'll go home early and the others will stay. That way she's not missing out too much.
My birthday party is coming up and I wanted to invite one of my friends but mum said that she does not like my friend. By Rachael (My friend) keeps barging herself into my plans with my other friends which are allowed to come How can I get Rachael to stop and let her down easy without her or any of my other friends hating me afterwards.