In English the progressive form (is ---ing) is mainly used for action verbs, where you actively do something. See http://www.bbc.co.uk/worldservice/learningenglish/radio/specials/1535_questionanswer/page4.shtml
First, "He sees the daughters" Has two meanings. One: He visually sees the daughters. .. which without context seems odd. Two: He is visiting the daughters. But apparently this isn't the meaning of the German sentence. German "sehen" must be literal. And yes. ..He is seeing the daughters could mean: 1) He's dating them,2) He's visiting them 3) He sees them visually. However without context it's a confusing sentence.
There are two difficulties in the word (I think). One is the 'ö' sound. It is like the 'i' in 'girl', but shorter. The second one is the 'ch' sound. There is no equivalent one in English or even anything that comes close. It is similar to the Scottish 'ch' in 'loch'. Like the 'g' it is a guttural sound, but the 'g' has the throat closed at the beginning of the sound and then suddenly opens it, which is called a plosive sound. For the 'ch' the air is flowing all the time, although it is a bit obstructed because the back of the tongue is close to the top of your mouth. It is not completely closed but the air needs to be forced through it. It might be easier to start with the beginning of a 'k' sound and then open the throat slightly so that the air starts flowing. Once you have that working, leave out the initial 'k' part.