JSFiddle - React, Tailwind, and code Playground

HTML

<fieldset>
        <legend>Click '+' to add fields horizontally</legend>
        <div id="slide-wrap">
            <div id="inner-wrap">
                <div class="horizontal-fields service-item">
                    <button class="addField">+</button>
                    <label>Text Box:</label>
                    <input type="text">
                    <label>Text Box:</label>
                    <input type="text">
                    <!-- Additional form fields are dynamically inserted here. -->
                    <div class="service-additional-fields">
                        <!-- Additional fields for DSL Tails -->
                        <label>Text Box:</label>
                        <input type="text">
                        <label>Text Box:</label>
                        <input type="text">
                    </div>
                </div>
                <div class="horizontal-fields service-item">
                    <button class="addField">+</button>
                    <label>Text Box:</label>
                    <input type="text">
                    <label>Text Box:</label>
                    <input type="text">
                    <!-- Additional form fields are dynamically inserted here. -->
                    <div class="service-additional-fields">
                        <!-- Additional fields for DSL Tails -->
                        <label>Text Box:</label>
                        <input type="text">
                        <label>Text Box:</label>
                        <input type="text">
                        <label>Text Box:</label>
                        <input type="text">
                    </div>
                </div>
           </div>
        </div>
    </fieldset>

CSS

#slide-wrap {
    margin:0 auto;
    overflow: auto; 
    background:#BCC5E1;
    border:1px solid #000;
}
#inner-wrap {
    float:left;
    margin-right:-30000px;/*Be safe with Opera's limited negative margin of 32695px     (-999em could cause problems with large font sizes)*/
    padding-left:20px;        
    width: auto;
}

div.horizontal-fields input,
div.horizontal-fields textarea,
div.horizontal-fields select,
div.horizontal-fields label {
    width: auto;
}

/* Horizontal fields is the class which is not re-sizing it's with correctly */
.horizontal-fields {
    display: block;
}

.service-additional-fields {
    display:inline-block;
}

JavaScript

$(document).ready(function(){
    $('.addField').click(function(){
        $(this).closest('.horizontal-fields').append('<label>Text Box:</label><input type="text">');
    });
});