Ask her this: is ridding herself of this "shame" by tripling your outgoings each month (for housing, that is) worth it?
Would she be willing to foot the extra cost, or is she expecting you to foot the bill for assuaging her "shame"?
Others have mentioned the relative "deadness" of rent and mortgage interest, especially in an interest-only mortgage, so tell your parents to, as it were, blow it out their ear, only more politely. In the short-to-medium term, you're better off renting, especially at housing association rents.
Tell her from me that not everybody else is a homeowner. I'm certainly not, and I find it very useful to be able to move at tenancy-end if I need to without all the hassle of selling and buying, and I'm a senior software engineer on a (very) good salary.
As to waiting for the new baby to be at school, or buying now, all I can say is that you should probably wait before doing anything rash and expensive, like buying a house in your position, or having another baby. Babies are expensive, you know, and it sounds like you can ill afford to have one at this time, especially since you will have to foot the bill all by yourself, without your wife's income.