If chapter 13 is filed, how does house get effected?

You can keep the house in a chapter 13 by including and past due payments in the plan. Since this house is way upside down, it's probably not a good financial decision to keep it.

You cannot modify the terms of a mortgage when it is for a primary residence. If the first mortgage is $300,000 for a house worth $175,000 you cannot reduce the mortgage claim to $175,000 without the mortgage lender's consent (Hint: they will not consent). If you cannot pay the note as it currently stands, you need to be honest with yourself and admit that and consider other alternatives because a Chapter 13 will only be a temporary fix before you lose the house (pretty quickly) anyway.

Chapter 13 does not allow you to force the mortgage company to accept less than you owe on the house, so the only way a chapter 13 would help is to allow you time to catch up if you are in arrears, and maybe buy you some time while you apply for a loan modification to reduce some of the principal or the monthly payment. Unless you can continue to make the regular mortgage payments and cure any arrearage in 5 years or less, it's too bad what the children want, you will have to move or work out a sell and rent back deal with the lender.

Surely you have discussed the options with your lawyer. If you have not retained a lawyer, it's almost always a good idea to do so, even at this point. If you are current on payments on the mortgage, then if you just keep paying (and say so in your Ch. 13 Plan), then nothing in the mortgage relationship should change. If you are in arrears on the mortgage, a Ch. 13 Plan can be used to make up those arrears in 60 monthly payments, usually without interest. You might want to make a hard decision which your children will not like, and that is to surrender the house to the mortgage-lender. Either get an agreement that they will waive the deficiency (very important) or surrender it through your Ch. 13 Plan.