When caring for poliwag, the most important thing you must do is establish its habitat. Poliwag need a lot of water and thus should be kept in either a heated pool or an aquarium. Be sure that you change the water on a regular basis, and keep the temperature of its habitat (not the water itself) at around eighty degrees Fahrenheit, or 27 degrees Centigrade. Poliwag need to keep their skin hydrated, and they’re very easily affected by temperature. Thus, it’s vital that you maintain the moisture and temperature of its enclosure. Additionally, this habitat should have a bit of solid ground lined with soft mulch (not gravel or cage filler, as with other pokémon) to allow your poliwag to come up and rest when it likes. You may also wish to add aquatic plants or a hiding space to make your poliwag feel more at home.
As for feeding, poliwag are carnivorous, and they prefer live prey, such as live crickets or other insects. However, if these aren’t available to you (or if you, understandably, can’t provide these), kibble will work just as well. Try not to overfeed if you give your poliwag kibble, as this may pollute their environment.
Once you set up its habitat and put it on a routine feeding schedule, caring for poliwag is actually quite easy. If given enough space, poliwag will be able to exercise themselves outside of battle training, and they’re perfectly content to sleep on the ground or in the pool you’ve set up. The only work you’ll need to put forth is to clean its enclosure and change its water at least once a week. This includes siphoning out old water, scrubbing down fixtures and the sides of its tank or pool with hot water, and adding new, clean(, preferably treated with special conditioners) water, as well as removing old food.
Finally, be sure to wash your hands before and after touching your poliwag—particularly before. Poliwag don’t drink; rather, they absorb moisture through their skin. While this is a great survival trick, it also means that they can easily be poisoned by toxins if pollution gets into their enclosure or if you happen to be wearing lotion or perfume. Washing your hands will minimize that risk.
As for your question concerning your mother’s lucario, it should be safe unless the lucario is exhibiting signs of stress or irritation whenever she interacts with your poliwag. If that’s the case, then you may wish to introduce your poliwag to her gradually and train your poliwag to be a bit less, as you say, touchy.
Best of luck, anonymous!
The Pokédex According to Bill 