He's right, in part. You and your child will inherit the house in various percentages. I suggest you insist upon a Will that gives you the house or put you on the deed with a right of survivorship.
Good luck to you and your family.
You need to check with a PA attorney who can tell you what the PA Statute of Descent and Disrtibution provides specifically.
I will guess that your mother-in-law will have no interest in the house, but that you and all three children or you and his daughter) will end up owning fractional interests. If any of the kids are minors, that will further complicate matters if it comes to needing the sell the house.
The most direct path is a survivorship or TOD deed, but those may not handle the mortgage issue they way he desires.
Legal counsel must be consulted directly.
Your husband is not correct. Under Pennsylvania law, if he owns the house and dies without will intestacy laws will define who gets his property and in what percentages. As for the insurance, the beneficiary designation will control unless it is payable to his estate. In that case, the intestacy laws will again split his estate between you and his children.
Finally, if you are going to transfer the house, and it is subject to a mortgage, you might want to see an attorney to make sure that the transfer does not accelerate the mortgage.
This does not constitute la legal opinion or legal advice. Please see your own lawyer and provide the specific facts of your case to your adviser.