My thoughts...
Stop your UC claim after first payment taking you over savings threshold.
Take from the $10,000 whatever you would have been paid in UC.
Save the rest.
Divorce your husband - do this asap before your savings build. Also pay for this from the money you are receiving.
Once the year is up, if you have taken 2 grand each month for living (24 grand), paid for divorce (5 grand) you should still have £90,000.
Plan to keep 24 grand to keep you for the year plus 16 for a savings buffer. This will give you a £60,000 deposit and a year to find a property and move in before you would start eating into the planned deposit money. (Bear in mind the quickest closing usually takes 3 months).
You will have to speak to a broker and explain your situation in detail to determine what mortgage you can get in your unique circumstances.
After you have have spent the 24 grand, start claiming UC again. Hopefully you will have your own home and 16,000 in savings.
Once you have all your ducks in order maybe you could use some money and treat the family to a holiday as well.
Congratulations and good luck 🤞