What is the Socio-linguistic Function of Mixing Pinyin and Characters Together By Adult Native Chinese Writers?
The 训读 (this jargon comes from Japanese) phenomenon is rare in Chinese, but it does exist, e.g. 廿 may be pronounced as èr shí (二十), 圕 as tú shū guǎn (图书馆), 哩 as yīng lǐ (英里). Doesn't that happen in English? Many people pronounce "etc." as "and so on", "i.e." as "that is", "e.g." as "for example". Traditionally, the function of 训读 in Chinese is to make difficult characters easier to pronounce and understand, but pinyin is rarely used in this case.

Recently pinyin used for non-standard 训读 in Chinese becomes popular, especially on the Internet, possibly inspired by the Japanese ACG (animation, comic, game) culture. It often suggests the deep, hidden meaning behind the apparent Chinese characters. The example in your post, 回家(xīn yì), suggests "coming home is a present (心意) for your parents". You can also find some funny examples like "丧(gan)心(de)病(piao)狂(liang)" -- it ostensibly reads "frenzied, crazy" but in fact the writer shouts out "干得漂亮, good job!" in his mind -- the effect is comical.

Besides, the reason why pinyin is chosen for denoting the implication may be obvious:


It can be easily distinguished from the Chinese character, so it doesn't disturb Chinese people reading the Chinese characters.
To a Chinese eye, pinyin is "hidden" at the first glance, so it is suitable for expressing the "deep" meaning behind those characters.