Is the wife justified in feeling distressed by her husband's forcing her to help him search for a second wife, and by his frequent online meetings with women under the pretext of a "Shari'a-compliant viewing before marriage," or is this feeling a demonic whisper, as the husband claims?

There is no objection to a husband marrying a second, third, or fourth wife if he is able to be just among them. The wife is not permitted to object to this, but she is not obligated to assist him. A wife is allowed to feel jealousy, but it is better for her to assist her husband as a kindness to him and to help him maintain his chastity. A husband's speaking with, dating, and meeting women for the purpose of marriage is not permissible if there is a risk of fitna (temptation/strife). It is permissible within the bounds of necessity for engagement, while observing Islamic regulations such as the prohibition of khalwa (private seclusion). It is preferable to follow safe methods for engagement. The wife should advise her husband while being keen on being a good wife to him and not falling short in his rights.