I understand that the most distant Phoenician settlement was Tarshish but I am wondering if the Phoenicians explored further than the strait of Gibraltar. I also am wondering why there were no settlements in the Atlantic especially considering the mineral resources of the British isles or West Africa.
"Tarshish" is meaningless these days. You are probably thinking about the settlement at Gadir (Cadiz), in what some call the Tartessos region of SW Spain. But that was not the furthest extent of Phoenician exploration to the West by any means. North beyond Gadir/Cadiz is the site at Dona Blanca, for instance. South of the Straits of Gibraltar, along the Atlantic Morrocan coast, was the Phoenician site at Mogador. I talk about it more here and here. There were probably sites even further down the Atlantic coast of Africa, but there is no initiative to do archaeology there and probably never will be.
Chellah, right outside of modern Rabat, was originally Phoenician. The ruins there, while mostly Roman, are pretty cool and they have massive storks.
The Atlantic is a lot rougher than the Mediterranean. The Mediterranean is no cakewalk but, for example, the waves on the Atlantic coast of Morocco are much bigger than the Mediterranean and the same is true of Spain, or for that matter, Mediterranean and Atlantic France. I think your use of the word constrained is a misnomer, the Phoenicians used the Mediterranean for trading. Sure they could have gone on longer trips, but it would have been higher risk and less reward than the developed trade in the Mediterranean.