We are replacing an underground electrical wire that shorted out which supplies power to our pool filter and pool house. In this same trench (18" deep and 175ft long) we would like to put a telephone and a cable line for TV and phone by the pool. Any problem putting these in the same trench?

No problem at all. For this length I would use at least two 1" conduits for the phone and TV.

Hardwire phone? Why not a cordless.

Hard wire phone will keep nosey neighbors at bay. And Extra Cat 5, you can have computer secure and fast. If it was me, I would also pull wires for Alarm, Future Alarm,
Keypad and zones. Maybe pull extra wire for pool video, could run camera through modulator, mix with cable and or satellite and view pool from any TV. It will keep you from worrying about the kids.
Outdoor motion as zone or chime , will notify house of activity at pool.