This is exactly what I needed. Thank you!
This is the final code I used on the child datapages. The style section hides the search form, while the script initiates a search that carries forward the filters from the parent datapage.
<style>
.cbSearchSpa {
display:none !important;
}
</style>
<script type="text/javascript">
document.addEventListener('DataPageReady', function (event) {
let buttons = document.querySelectorAll(".cbSearchButton");
//adding onclick event listener to the 1st DP search form
buttons[0].addEventListener("click", ()=> {
//clicking on search button of 2nd DP with a delay
setTimeout(()=>{buttons[1].click();}, 500)
}, false);
});
</script>