You have no obligation according to Fiqh standards. The matter of honesty and friendliness and... with your spouse is something else. You have to manage it according to her types of manners and how demanding she would be in future.
No, there is no issue at all with doing nikah contract outdoors, or in morning.
The only time it is makruh is when the moon being in the zodiacal sign of Scorpio (qamar fi al-'aqrab), and when the moon is absent (end of lunar month/beginning of lunar month), which is called al-mihaq.
You need to take them to an authentic scholar who can explain for the the Islamic rules according to Ahlul Bayt (AS) and tell them that following Ahlul Bayt (AS) is much more important than following the culture or society.
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