getResources not working properly with snippet

You do it wrong. You need to use 3 TVs with type «image» with correct paths to files.

Or you could try to use pdoResources with &prepareSnippet that will additionally process each row:

[[!pdoPage?
	&element=`pdoResources`
	&parents=`219`
	&tpl=`MATCH_INDEX_FREE_TPL`
	&showUnpublished=`0`
	&showHidden=`1`
	&limit=`5`
	&processTVs=`1`
	&includeTVs=`IMAGE,Race`
	&depth=`25`
	&sortby=`createdon`
	&sortdir=`DESC`
	&prepareSnippet=`getMyImages`
]]
[[!+page.nav]]

Snippet getMyImages:

<?php
// $row - is the array with resource selected by pdoResources being processed now
$values = explode(',', $row['tv.IMAGE']); // Your selected TV with images
foreach ($values as $k => $value) {
	$row['path' . ($k +1)] = $value; // Add new placeholders to $row
}
return json_encode($row); // Return data with additional placeholders

Now you can use placeholders in chunk:

<div class="dog_cont">
	<div class="data_title_new">[[+tv.Race]]</div>
	<div class="dog_photo2">
		<div id="ad_image_big">
			<a href="[[+path1:phpthumbof=`w=900&zc=t`]]" rel="lightbox"><img src="[[+path1:phpthumbof=`w=200&h=160&zc=t`]]" /></a>
		</div>
		<div id="ad_image_small" >
			<a href="[[+path2:phpthumbof=`w=900&zc=t`]]" rel="lightbox"><img src="[[+path2:phpthumbof=`w=95&h=80&zc=t`]]" /></a>
		</div>
		<div id="ad_image_small2">
			<a href="[[+path3:phpthumbof=`w=900&zc=t`]]" rel="lightbox"><img src="[[+path3:phpthumbof=`w=95&h=80&zc=t`]]" /></a>
		</div>
	</div>
</div>

No need to make them uncacheable, by the way.

There could be a misunderstanding with letters case of your placeholders, but you can see them all if you will specify a blank &tpl=`` property.

pdoPage and pdoResources is the parts of pdoTools package.

You can use snippet as modifyer of IMAGE TV

<div class="dog_cont">
<div class="data_title_new">[[+tv.Race]]</div>
<div class="dog_photo2">
<div id="ad_image_big"><a href="[[+tv.IMAGE:IMAGE_PATH=`1`:phpthumbof=`w=900&zc=t`]]" rel="lightbox"><img src="[[+tv.IMAGE:IMAGE_PATH=`1`:phpthumbof=`w=200&h=160&zc=t`]]" /></a></div>
<div id="ad_image_small" ><a href="[[+tv.IMAGE:IMAGE_PATH=`2`:phpthumbof=`w=900&zc=t`]]" rel="lightbox"><img src="[[+tv.IMAGE:IMAGE_PATH=`2`:phpthumbof=`w=95&h=80&zc=t`]]" /></a></div>
<div id="ad_image_small2"><a href="[[+tv.IMAGE:IMAGE_PATH=`3`:phpthumbof=`w=900&zc=t`]]" rel="lightbox"><img src="[[+tv.IMAGE:IMAGE_PATH=`3`:phpthumbof=`w=95&h=80&zc=t`]]" /></a></div>
</div>

IMAGE_PATH

if (!$input) return '';
if (!$options) $options = 1;
$values = explode(',',$input);
if (isset($values[($options - 1)])) {
  return $values[($options - 1)];
}
return '';