I agree with Natja. This sounds like a terrible situation.
If she wants to leave, then she should leave. It seems to me unreasonable to require her to stay when she does not want to - and also, possibly illegal if she is being held against her will.
If the husband is not attracted to her as she is (e.g. weight requirements) then it is best if he does not pursue a relationship with her. Even if she manages to get the weight off that he wants her to lose, there is no guarantee that she will be able to keep it off. It is much easier to put on weight when you have been overweight than when you have never been overweight, and much more of a struggle to keep weight off than to never put it on in the first place. As she gets older, and at stressful times in her life, it will be more difficult for her to keep the weight off, and to pressure her about it, or make her feel less desirable as she gets older would be cruel. Love her as she is, or leave her alone.
Supposing that a real attraction exists between them and they choose to go ahead with getting married (this sounds like a polygamous situation rather than polyamorous, so I use 'married') - then the differences in domestic routines etc would suggest that it would be better for the 1st wife and 2nd wife to live in separate homes. There are relationship stresses, and then there are living together stresses, and living together stresses can come to be mistaken for relationship stresses when people live together. I think it's best to keep them separate and work on one at a time.
I think it is unreasonable to expect to have the input of a parent over another person's children unless that person has asked you to have that role in their lives and you are very well-known to the children and accepted by them. In any case, it is certainly impolitic to strongly criticise how another person is raising their children unless you know them very well indeed (as in, have known them well for several years). Making a suggestion may be acceptable, but assuming that you have the right to tell them how to raise their children is unreasonable.
It is worth remembering that this woman has lived her life independent of the man's influence and requirements up until now. She is accustomed to being in control of her own life, her own home, her own children and her own destiny. If she chooses to willingly give that up, then that's fine. But to insist that she give up elements of autonomy that she is accustomed to seems unreasonable. She is a whole human being with a history of her own, which needs to be taken into consideration. Any changes should be negotiated, not demanded. And negotiations should mean that there is give and take on both sides, with allowances made for each person's needs.
The children have reason to expect that their parent/s will be consistent in their approach, whether that approach is heavily disciplinarian or fairly lax. It's unlikely that the children will respond well to sudden, heavy-handed discipline if they have been unaccustomed to it. This, and their misery, would add to the burden of the woman who is already trying to adjust to a very different way of life.
Under the circumstances, when the man feels that she 'is not a fit for their family' and the woman just wants to go home, it seems pointless to insist upon her finishing out her time. The experiment has been run, and it has brought definite results, just earlier than expected. It has performed its purpose, and it is time to move on.