In addition to what's been said above re. experience and portfolio work, The OP should also consider a more focused taught Masters in Web Technology or similar: it'd be cheaper and can be done via distance learning whilst you build up a portfolio. MOOCs can fill any transitional gaps you may have.
However, if your heart is set on another full undergrad degree, consider earning and learning. Part-time Computing and IT students are exempt from the ELQ requirement regarding previously obtained degrees, so SLC might fund you again; make a short-list of courses and call the providers/SLC to make sure. This may be a fairly long-winded route towards what you want to do though.
Do decide whether you want to do front-end or infrastructure/systems work in advance, as these two streams diverge. The former is technology crossing over into applied arts and humanities, with some industrial psychology; the latter has more CS meat to it, and may appeal more to an ex-engineer.
Titles of programmes to browse would be:
Computer Science
Computing
Internet Computing
Web Technologies
Online Computing
Web Development
Cloud Computing
Web and Distributed Systems
Web and Mobile Development
Business Information Systems
and variations of the above. For the more theoretical routes, pick up and skim through a good introductory book on Discrete Mathematics before your course starts.
Edit: Most of these are essentially under the umbrellas of Computer Science and Software Engineering. The veritable alphabet soup of qualification names these days is primarily a marketing exercise to attract people to what may be perceived as hard 'traditional' tech subjects.
Have fun!