I am so sorry to say that if dad did not leave a will, his wife probably has priority over kids as regard disposition of the ashes. But if no will, and if dad had any separate property, you would be entitled to 1/2 of the separate property if you have no siblings. Separate property would be any property your dad had before his marriage, and that he did not commingle. This is a general response and other pieces of property might or might not be separate. You need to consult with an attorney...
You can go to the recorder's website and check title on the property. If the aunt held the property in joint tenancy with her dad, then she could have transferred title to her following his death by submitting an Affidavit of Death of Joint Tenant. Otherwise, she could not have transferred title. If your husband's mom is the named executor, she should meet with an attorney familiar with probate.
It depends how the property is titled. If the three of you are joint tenants, you must record a Death of Joint Tenant, with the Death Certificate, with the Recorder's Office. That will leave the property in the remaining two names. If the Deed is Tenants in Common, then your mother's share must be set aside or probated depending on the value of the property.
If you did not sign anything assuming financial responsibility, and if no estate was opened for your aunt, you should return the bill and write on it that the person named is deceased and that there is no estate. You are not responsible.
If there is no estate to probate, then you do not open one. You are not liable for his debt. If an account is later discovered, and the amount is less than $20,000, you can do a Small Estate Affidavit and submit it to the bank along with a copy of the death certificate. And yes, if accounts were joint, they go to the survivor.
What is your question? If you want to file for divorce, do so. You still have one minor child so child support will be required. The amount and who pays it is dependent on the custody time share and the incomes of the two of you. Best to talk to a family law attorney to know options and process.
It is irresponsible to answer these questions without a complete review of the estate, the will, the assets, etc. The other attorneys are absolutely correct. If you do not have a probate attorney, you should consult with one immediately. You have a fiduciary duty to the beneficiaries/heirs of the estate.
Options are that you reach out to him and ask him to sign a Consent for step-dad to adopt. Tell him this is what daughter wants, or file a Petition to Terminate his Parental Rights, or wait until she is 18 and step-dad can do an adult adoption without bio dad's consent or notice.
If the child has been in Nevada less than 6 months, jurisdiction remains in Illinois. Once the 6 month mark hits, assuming no custody orders out of Illinois, Nevada will have jurisdiction. If you can't provide for your child at this time, you are still entitled to a relationship. If you can provide, you should pick up your child and return to Illinois, or file a custody action in Illinois.