Hello @ArraDreaming , @Rhye , @Eve7 , @Molly22
@ArraDreaming, some of the suggestions offered by Rhye, Eve and Molly have also worked for me.
Possibly, another way of approaching your situation, or that of anyone else, is to consider what is actually happening for you in the time leading up to and including your own regular sleep time.
From your description of your own situation, I would think that you may have established a pattern of being in a constant state of preparedness/arousal for attending, in particular, to your 4 yo. A situation that appears to have been a major influence on your sleeping capacity and pattern for at least that time and possibly earlier, during your wife's pregnancy. This has been compounded by the need for attention to your younger child. It may be possible that the 4 yo old is actually sleeping better now, because of the presence of your younger child, who seems to have established a regular sleep pattern more quickly than your 4 yo. Unfortunately, leaving you out of that loop, it appears.
Circadian rhythms {see Addendum below} can also be disrupted by external influences and take time to 'recalibrate' and re-adjust when those influences become less intrusive.
In your description, you have not indicated whether you are on your own, or have support with the children, given by a spouse/partner/companion. What sort of support, if it exists, is contributed?
Did you ever have trouble sleeping before the arrival of the children?
Based on the information you have offered, it appears that lack of sleep is definitely a significant concern. It is common knowledge that having sufficient sleep, or lack of, has effects on everything we do during the day. However, the reason for lack of sleep may be addressed simply by re-establishing a regular sleep preparation pattern.
Oddly enough, it is likely that the more you work at trying to establish sleep, the less likely it is to occur due to the attention and mental application that the issue is being given. Preparation for sleep, I believe, has to be planned ahead and then the plan 'mindlessly' followed. The less attention that you give to each nights preparation, the more effective will be the process of preparation. The process should become a habit to be followed without attention. This means that you remain aware of what is going on around you and can raise your level of alertness, but only if the need arises.
Using the ideas already offered, it may also be worth considering a carefully chosen, prescribed and monitored sleep assist medication. Or possibly even, a low dose of an anti-depressant, if you feel that anxiety may be a contributing factor with the sleep issue. Neither of these should prevent you from attending to the children as required. In low dosages, they should also be easy to reduce and discontinue as your sleep patterns improve. I know this from personal experience. For this, a doctors guidance and assistance would be required.
If you feel that there are any other factors that are influencing your sleep patterns, that people offering suggestions may take into account, please let us know.
With Best Wishes
@HenryX
Addendum: {Links can be accessed directly from this note.}
Extract from: https://www.webmd.com/sleep-disorders/find-circadian-rhythm
"Although you won’t hear it tick, your body has its own clock. The physical and mental changes it causes are called circadian rhythms. Most living things have them, including animals, plants, and even some germs.
Circadian rhythms affect your sleep patterns as well as other ways your body works, like your hormones, body temperature, and eating habits. When they get out of sync, they might also cause problems with your health. They’ve been linked to different disorders including diabetes, obesity, and depression.
To get good, healthy sleep, it helps to know what keeps your body’s clock on track and what might throw its rhythm off."
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