There are some good answers for managing volume if you must use an acoustic kit. However in your question you also asked about an electronic kit (I'm not sure why they don't call them digital). I know you mentioned the absence of mic or speakers, but also mentioned a digital piano which means you will have speakers for the piano.
I have a band that plays classic rock, pop, and country music in small venues. I have used four different drummers and all of them used an electronic kit. For whatever it's worth, all the kits were made by Roland, but I understand Simmons makes some really good electronic kits as well. The venues we play (resturants and bars seating less than 100 people) require relatively low volumes. Whenever I watch other bands in these same venues that have an acoustic drum kit, folks complain that the volume is too loud because the rest of the musicians have to turn up their volume to be heard above the drummer.
The technology in electronic kits is continuing to evolve and drummers tell me the makers of these kits are getting better at replicating the feel of an acoustic kit. The main advantage for a drummer using an electronic kit is that you don't have to hold back and can put your full energy and velocity into your drumming - while controlling the volume with a volume control knob. I can tell that when a drummer tries to play softly on an acoustic kit, it seems to interrupt their rhythm or impede there technique and they are not as smooth on the fills and transitions and faster runs.
For amplification you can use a specialized electronic drum monitor. These are tuned and designed specifically to accurately reproduce the full range of sounds found in a full drum kit. Many have separately amplified woofers for the kick drum plus high range tweeters for the cymbals as well as mid range for the toms. You can position one of these so that the audience can hear it as well as you do. Most also have headphone jacks.
Depending on how your digital piano is amplified, you may be able to input your drum kit into that system. My drummers plug into my PA system and we EQ their channel for optimal sound of their kit and adjust the volume so that it can be heard in the overall mix without overpowering. One of my drummers brings his own drum monitor as well - and in other bands he plays in sometimes uses it as a standalone amp for his drums and does not go into the PA at all.
It might take getting used to the feel of an electronic kit (or V kit as they are sometimes called), but it is certainly an option for managing and fine tuning the volume without having to hold back your energy. Plus you can plug in the headphones and practice at home while others are sleeping or watching TV.
They work great for recording too - you don't have to worry about getting multiple mics positioned just right. You have individual volume control over every drum in the kit. One more nice feature - you can literally have 100 different sounding kits in one. Need congas or timpanis - no problem - just select them on the console.
I have included a picture of a monitor specifically made for V drums below.