From your question it isn't very clear if you have GTM deployed on wordpress already or not. If not, get it on there via a plugin or by editing the template code to add the GTM code.
As far as getting sudomain.domain.com traffic to appear in the same analytics view, you need to use the same UA code in
Tracking ID field of the the
pageview tag in GTM and modify one thing. Specifically under
More Settings -->
Fields to Set add an entry with
cookieDomain as the Field Name and
auto as the Value. This will cause google to push pageviews to the same Google Analytics Account and event connect the same session since the
auto part will cause GTM to set the analytics cookie to the highest domain it can which on
sudomain.domain.com will resolve to
ga('create', 'UA-XXXXXXXX-Y', 'auto');
The cookieDomain part is in this line
ga('create', 'UA-XXXXXXXX-Y', 'auto'); with the UA code being the same you use on the domain.com site.