Most of the time, for events like this you have to "audition" for a part, the princess company may not have responded because they also have an image to uphold and sometimes they don't want people who don't fit that image to be associated with their company even if you aren't at the event as a part of the company people will always assume.
When sending emails to any party entertainment company trying to get a piece of the cake make sure you do it as if you were auditioning for a big part in a play or auditioning for a part in their company even if you aren't and just want to participate in the event. Send a very good email with a hook in it, be enthusiastic, and infom the company of what you can offer and that you will hope to be able to work with them on the event. Along with the email send photos of yourself and make sure they're very flattering, princess companies are all about look. They want people at the event who will make them look good and not have parents fuming at the mouth that they hired a random person who looks like a civilian who just put on a tail to get near kids. Send photos of your tail too, sale yourself to them,this is your sales pitch.
If you still can't get in the event, don't feel too bad, you just have to find something else. Make your own event, do a reading at a library, Earth day is coming up, do an Earth day meet and greet, you're your own PR person so if people don't know there's a merman for hire then you need to let them know.
A good pitch will be:
Hello <insert name>!
My name is <name>, I am very interested in an event that you will be hosting soon, <event name, date> at <event location>. I am a professional merman here in the <where you live> area with history working with children of all ages. I am very professional and believe that the event will be livened up and more unique with a merman making an appearance. I mostly provide birthday parties for children so children are my main audience, I can play games and entertain them when the other entertainers are too busy or have too much on their hands. I can also offer photo sessions and a merman meet and greet for both the adults and the little ones.I have included photos of myself for you to review, thank you so much for your time, I hope to hear from you soon.
With care,
<Insert your name>
<Insert mer name>
<email address>
<phone number if you have a business one>
<website (I suggest making a separate website that isn't a facebook page, it seems more professional)>
<Logo if you have one>