People often don’t even think about the kids in these situations. Kids from temporary marriages are going to grow up prob never knowing their father but who cares, right, cos at least the sex was halal 
An Arab friend of mine was telling me that a lot of men actually use temporary marriage as a means of making time they spend with prostitutes halal. There are parties in London where the girls are handed envelopes of money, go off to have sex and this is all done under the umbrella of misyar..
In societies where polygyny is more accepted and widely practised families tend to become fragmented (rich husbands often decide to ‘trade in’ wife no.4 for a newer model when they get bored) and I’ve seen the effects it has on the kids, they often end up bitter and resentful..If everyone is ok with the arrangement (yes there are wives out there who actually encourage their husband to take another wife) I don’t think it’s a bad thing but I still find it quite hypocritical us Muslims like to bleat on about how messed up Western society has become due to single mothers bringing up kids on their own etc and then we go on to promote a system that effectively makes those previous wives (with their kids) live a similar lifestyle with a father figure there only 50% (at the most) of the time…
I can’t imagine myself being able to look after teenage sons without their dad around to guide them. I wonder what happens when kids from one partner get ill or get into trouble at school or need extra attention from dad for some other reason but he’s supposed to spend the exact same time with each wife and family… Sounds like it could get messy..