Hi there,
I am sorry to hear that you are having such a difficult time. I understand how tiring this could be. I have a 3 month and a 21 month old who sleeps very well but I'm still tired and a little sleep deprived. I can only imagine how challenging this is for you.
I agree with everyone who has said that your baby needs more sleep. I am mum of 4 with a nearly 16 year old, 13.5 year old, 21 month and a 3 month old. All 4 of them have always naturally slept well and I have always been really strict with my sleep routines.
Firstly, my 3 month old doesn't spend more than an hour awake at a time. For 10 month olds, I wouldn't allow them to be awake for more than 3-4 hours at a time.
For example, if my 10 month old woke up at 6am, I would be putting him for a nap between 9 and 10 am. If he wakes up at 11am, I would put him for a 2nd nap at 2 or 3pm latest then bedtime at 6 or 7pm. I would allow for 30 minutes on either side but no more than that.
I don't have a fixed time unless my baby sleeps and wakes at the same time every day. I actually count the hours and set my bedtimes based on that. This has always worked for me as it prevents my babies getting overtired. On the rare occasions when I'm unable to stick to these times, my baby became very fussy and difficult because of overtiredness.
Babies don't know that they are tired and need to sleep so they'll stay awake for as long as you allow to them to. They may eventually fall asleep but not all babies do.
I agree with the person who advised that gradually allowing your baby to self soothe will help. I don't rock or hold my baby for her to sleep. I place her in her crib and walk away. She sometimes makes sounds or fusses a bit but eventually settles. I sometimes use a cot mobile to play the same music each time my baby goes down to sleep and this helps to soothe her if she's fussy.
I only rock if we're away from home and she's refusing to settle. In situations like this, she fights and is hard to settle but I hold her close and firm against my body to comfort her and she eventually sleeps.
Babies / children thrive on the same routine each day. Try putting your baby in his own bed and stay in the room so that he can see you. Co-sleeping makes it harder. If he starts to cry, talk or sing but don't remove him from his bed (he will get used to you taking him out when he cries so he will keep doing it).
Try using a night light rather than having the room fully lit. Don't ever turn on the full light during bedtime. Keep the room nice and dim.
When he wakes up at those weird hours, don't take him up from his bed. Simply lie him down and say it's time to sleep. Night night. Things like that. Do all you can to avoid taking him out of bed.
Every child is different but young children are very difficult when they're over tired.
I also keep my baby's sleeping environment very quiet and free from distraction. My baby would be asleep upstairs while everyone else is downstairs. I use a baby monitor to check in. I try to keep all noise to a minimum.
My 3 month old sleeps through the night since 5 weeks old. All of my children slept through the night at a young age. I feed on demand when they're hungry and allow them to sleep as much as they need. I don't wake them up. I amend sleep times as necessary whether that's making them early or later.
Make your baby wake time windows shorter and encourage more sleep. It will be hard at first but will change if you stick to it. I have used these tips to help others as well.
I really do hope that things improve for you, your baby and family. Take care.