My own recommendation is to go and see a solicitor to discuss this, or post in the legal threads, you will get a lot of uninformed but well meaning advice otherwise.
Nobody can force you to accept a Mesher order or the 50/50 split he wants, and considering you have 3 children and have a low income there is a very strong possibility you will get more than 50%.
The fact that you have not contributed to the mortgage because you were a SAHM doesn't matter (as long as you are married) as your contribution to the marriage is in kind, you took care of the children so he had the space and opportunity to develop his career.
Please note however that the distribution of the assets will be about trying to achieve a fair split, so the court will also consider his needs and circumstances. So f he is not earning lots of money ether, it may be that the fairest split is 50/50.
Whether a Mesher order is good or not, it depends in a number if factors, like your age, the age of the children, and your possibilities of being able to support yourself independently after it comes to an end.
I wanted a Mesher order and didn't get one. I know now it was for the best. It took a lot of sacrifices to be able to buy his percentage of the house (even when he got a very small percentage). But the house is now mine and is also a possible source of income. Had I been given the Mesher order I would have been too old to apply for an affordable mortgage at the end of it, and I would have been feeling under his "hold" for many years. I understand why you don't want it.