Sankoku has むずがる.

@@ -12 +12 @@
-<reb>むつかる</reb>
+<reb>むずがる</reb>
@@ -15,2 +15 @@
-<reb>むずがる</reb>
-<re_inf>&ik;</re_inf>
+<reb>むつかる</reb>

I don't think [nokanji] is needed for むずがる. Should be marked as irregular.
むつかる is in all the refs. Shouldn't be hidden.

@@ -12,2 +12 @@
-<reb>むずがる</reb>
-<re_nokanji/>
+<reb>むつかる</reb>
@@ -16,2 +15,2 @@
-<reb>むつかる</reb>
-<re_inf>&sk;</re_inf>
+<reb>むずがる</reb>
+<re_inf>&ik;</re_inf>
@@ -23 +22 @@
-<gloss>to fret (esp. of infants and small children)</gloss>
+<gloss>to fret (esp. of a young child)</gloss>

@@ -23 +23 @@
-<gloss>to fret (esp. infants and small children)</gloss>
+<gloss>to fret (esp. of infants and small children)</gloss>

むずかる	3588	61.4%
むつかる	502	8.6%
むずがる	1756	30.0%

I suggest merging むずがる (2783380) here, and making 憤る [rK] (I feel like [sK] but the kokugos have it.)
If approved, 2783380 needs to be deleted.

@@ -6 +6 @@
-<ke_inf>&oK;</ke_inf>
+<ke_inf>&rK;</ke_inf>
@@ -11,0 +12,4 @@
+<reb>むずがる</reb>
+<re_nokanji/>
+</r_ele>
+<r_ele>
@@ -12,0 +17 @@
+<re_inf>&sk;</re_inf>
@@ -17 +21,0 @@
-<xref type="see" seq="1504640">憤る・いきどおる</xref>
@@ -19,2 +23 @@
-<s_inf>this kanji reading is restricted to infants, small children, etc.</s_inf>
-<gloss>to fret</gloss>
+<gloss>to fret (esp. infants and small children)</gloss>

Maybe I shouldn't copy/paste the whole explanation, but who knows which site will outlive which, and it's a good set of comments.  

辞書によると憤るの訓読みは「いきどおる」と「むずかる」がありますけど...
https://ja.hinative.com/questions/13468854
「むずかる」の読みは常用指定されていないので、公文書や新聞などではひらがな書きされます。
一般の使用に制約はありませんが、マンガやラノベ以外の本は読んだことか無いような人も増えており、「憤る」に「むずかる」の読みがあることを知らない、とか、そもそも憤る赤ん坊自体見たことがない、などということも（書き手の側も含め）珍しくはないと思います
2
上述の通り、公文書、新聞では必ずひらがな書きされますので、「憤る」と漢字交じりで書かれていたら、必ず「いきどおる」です。一般の書物では文脈で判断するしかありませんが、「むずかる」は乳幼児か、乳幼児に擬せられた者に対してしか使われませんから、判別は容易だと思います

I can't mark kanji forms [rK] on a [uk] entry, but I'm pretty sure [oK] still applies.   If the random hinative reference is to be believed, this is a word with an official orthography, and it's hiragana. 憤る in a newspaper will *always* be いきどおる.

As some confirmation, sankoku does not give kanji for this term at all (and it contains some crazy kanji, like 憤懣).  Everything I've looked at suggests 憤る will be taken as いきどおる in modern Japanese, and even in old texts, 憤る will only be read as むずかる when discussing babies and small children specifically. (sankoku says "小さい子供などが"...)

Right now 憤る appears to have an ambiguous reading(which is exactly why the hinative question was posed).  It would appear that it's not really that ambiguous, and we can easily clarify this for anyone who sees both 憤る entries here.

More stats on backref (I started there first before finding the hinative details).  I recommend merging.  We don't *usually* have standalone entries for prescriptive "mistakes", and the kokugos identify the backref as a common misunderstanding/error, which might be better as [sK] or [io] to here.

@@ -5,0 +6 @@
+<ke_inf>&oK;</ke_inf>
@@ -15,0 +17 @@
+<xref type="see" seq="1504640">憤る・いきどおる</xref>
@@ -16,0 +19 @@
+<s_inf>this kanji reading is restricted to infants, small children, etc.</s_inf>