B.M.
What about a Sit and Stand stroller? Your younger child can be in front and your 2 year old can sit or stand in the back. It has straps so he can be belted in if necessary.
(oops! I read "5 month old AND wheaton terrier. Sorry for the confusion!)
We have a Baby Trend one from Target. I love it and would highly recommend that you look into them.
Hope this helps,
B. :-)