Your elders would be requesting you repeatedly to send them to old age home as they are getting bored at home. The reason could be that they are getting bored by sitting alone at home. At the old age home, there would be people of their age group and hence they would have the chance to share the same sort of emotions, likes and dislikes. It does not mean that they do not want to stay with you. They would prefer to stay with you provided they are comfortable staying at your house. Though you procure them the best bed, cook the delicious dishes they like, if you could not spend time with them when they are suffering from some ailment then it would be miserable for them.
They could not ask you to spend time with them seeing the struggle in your life to settle down in job. At least, if they are treated well by gifting the mobility scooter they would be happy than hiring a care taker. When you hire a care taker they might feel inferior and would try to avoid accepting the truth that they are getting older and want to try their best to move around by self which is more dangerous for them.
Hence, do not create any situation that would make them feel bad and thereby feel embarrassed. They might be wondering and would even get disappointed by the fact that they are losing their capacity to move around. By buying the scooter you could handle the situation in a much better way. You would be giving them the confidence that they could lead the life without the support from another person. Elders with confidence would be self-independent than troubling everyone else who is staying in the house.