Of course he (son-in-law) can stay and visit the wife parents home other than gender mixing issues that you have mentioned. In fact this is very common in few sub continent families that son-in-law permanently stay in wife house due to financial reasons. There is a term called "ghar damad" in Urdu and Hindi that means "Son in Law stays in wife's parent home or wife's own home after marriage".
The idea of "Ghar damad" happen when usually the husband is poor than wife's family, and the parents of the wife in order to support their daughter bear their accommodation and other expanses. Some rich parents would even buy whole home for their daughter and son-in-law to live in. I don't see why Islam would be against it, unless Islam tells women to marry a rich person always. Parents providing expanses for them would be considered sadaka. Source
It is more of a problem in Islam that the wife stay in the husband's parents home, due to gender mixing issues as you mentioned. Islam strictly prohibits that wife meet non meheram in-laws. There is a very famous hadith in Islam in which prophet Mohammed (PBUH) called brother-in-law death. Wife should avoid contact with him in all circumstances. If wife demands a separate accommodation, then it's husband's responsibility to do so.
I hope God guide us.