Entertaining a 3 1/2 year old and 1yr old

Try Ooblek with the oldest one. Great fun! www.youtube.com/watch?v=LyDUr0DN1es
The youngest one will like simple toys like small balls, or corks, tearing paper, banging things together to make noise etc.

Best bargain I ever got for my three grandsons was a little plastic barbecue which was half price in Tesco. All three of them loved it and the youngest one, who is five, still gets it out when he comes round. Endless plastic sausages and burgers cooked and served up!
Cardboard boxes of all sizes are always a winner, coupled with blankets to make a den if they are big enough, and lots of paper and crayons.

library time............making cakes. let them help. messy but fun.get a sand pit...

DGD has a little shopping trolley and a till and we spend about 45 minutes going to Aldi, Tesco, Asda and Sainsburys (utility room) to buy stuff (boxes DD has saved from shopping), taking it home (playroom) - and then Disney princess sleepovers in her bedroom with duvets etc dragged off bed to make a den. She is 2 and DGS 5 (now at school but on holiday). DGS scorns the Disney princess play but has on occasion initiated it. Lots of board games - she doesn't really understand but has to do the same as big brother so you put them out and she does whatever she wants then tidies away, parks - lucky to have 3 in walking distance, DGS2 is 1 and happy to run around any grassy area with a ball, plays with duplo cars a lot, empties my "safe" cupboards. Older 2 like play dough, helping - washing dishes, baking, soup. All like going to library. 1 year old spends 20 minutes "sorting" washing - it's very funny! 5yo has helped Papa remove snails from garden since he was 3 - humanely placed over wall into grounds of care home. When I was much younger my flatmate was a primary school teacher and we all collected things like cardboard boxes, loo roll middles as she had her day divided into 10 minute intervals because that was the time span a 5 yo would concentrate and this has stayed with me all my life for my own children and now grands.

Gosh you are brave! Do you have a free bus pass? If so, could you take them both 'upstairs' on a long-ish bus ride?
It depend how much luggage you have to carry with them but we found that a great experience when ours were under fives as nowadays they go everywhere by car and never see the world from upstairs on a bus.
Another crafty move I have (naughty Grandma!) is that ours are girls and love having their nails painted! They spread their hands out flat on the table and I dab a bit of nail varnish on each nail. It is amazing how long it takes for Grandmas to say it's dry enough for them to move
Seriously though - they are young which makes it difficult. I buy puzzles and books from charity shops for their toy box so there are usually 'new' things to discover!
Good luck! I will be interested to see other suggestions!