2 things you can do.
First, download an app like Caffeine to keep your Mac awake even when the lid is closed. Do not activate the features in Caffeine when moving your Mac around because of risk of damage to the HDD. If you go this route, you gotta remember to disable Caffeine when carrying your Mac around and when transporting it.
OR
Second, purchase a wireless mouse to wake your Mac up out of sleep. This is what I use and for my MBP, I have found it's best to wait a good 5-10 seconds after I close the lid to wake it up again or else it doesn't want to wake up for some reason. My Logitech wireless mouse was about $15 at Best Buy. After you've used the wireless mouse to wake your Mac up, you can continue using your remote mouse app to operate it.