HTML email align text

Honestly, if you're doing an HTML email I'd stick to using tables. Not all CSS selectors are available in all email clients and you'll drive yourself mad trying to do it any other way. HTML emails are like the web 5 years ago.

There are a couple of good documents on the subject:

https://www.campaignmonitor.com/css/

http://www.emailology.org/

For your example:

<td>
  <table cellpadding="0" cellspacing="0" width="100%">
    <tr>
      <td align="left">First part</td>
      <td align="right">Second part</td>
    </tr>
  </table>
</td>

It's horrible but unfortunately it's still the best way.

<p align="right">My right content</p>

It should do the trick as it is HTML1.

Use (shudder) layout tables.

Outlook's support for styling of email is so awful that there isn't any other way.

There is a 24 ways article with some general advice for writing HTML formatted email.